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Operational Calculus And Generalized Functions

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Operational Calculus and Generalized Functions

Operational Calculus and Generalized Functions Book
Author : Arthur Erdelyi
Publisher : Courier Corporation
Release : 2013-07-24
ISBN : 0486316327
File Size : 52,7 Mb
Language : En, Es, Fr and De

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Operational Calculus and Generalized Functions Book PDF/Epub Download

Suitable for advanced undergraduates and graduate students, this brief monograph examines elementary and convergence theories of convolution quotients, differential equations involving operator functions, exponential functions of operators. Solutions. 1962 edition.

Operational Calculus and Generalized Functions

Operational Calculus and Generalized Functions Book
Author : Arthur Erdelyi
Publisher : Courier Corporation
Release : 2013-07-17
ISBN : 0486497127
File Size : 32,8 Mb
Language : En, Es, Fr and De

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Operational Calculus and Generalized Functions Book PDF/Epub Download

"Based on a math course for advanced undergraduates and graduate students at Cal Tech, this brief monograph requires a background in advanced calculus. Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, exponential functions of operators, and problems in partial differential equations. Includes solutions. 1962 edition"--

Integral Transformations Operational Calculus and Generalized Functions

Integral Transformations  Operational Calculus  and Generalized Functions Book
Author : R.G. Buschman
Publisher : Springer Science & Business Media
Release : 2013-11-27
ISBN : 1461312833
File Size : 31,6 Mb
Language : En, Es, Fr and De

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Integral Transformations Operational Calculus and Generalized Functions Book PDF/Epub Download

It is not the object of the author to present comprehensive cov erage of any particular integral transformation or of any particular development of generalized functions, for there are books available in which this is done. Rather, this consists more of an introductory survey in which various ideas are explored. The Laplace transforma tion is taken as the model type of an integral transformation and a number of its properties are developed; later, the Fourier transfor mation is introduced. The operational calculus of Mikusinski is pre sented as a method of introducing generalized functions associated with the Laplace transformation. The construction is analogous to the construction of the rational numbers from the integers. Further on, generalized functions associated with the problem of extension of the Fourier transformation are introduced. This construction is anal ogous to the construction of the reals from the rationals by means of Cauchy sequences. A chapter with sections on a variety of trans formations is adjoined. Necessary levels of sophistication start low in the first chapter, but they grow considerably in some sections of later chapters. Background needs are stated at the beginnings of each chapter. Many theorems are given without proofs, which seems appro priate for the goals in mind. A selection of references is included. Without showing many of the details of rigor it is hoped that a strong indication is given that a firm mathematical foundation does actu ally exist for such entities as the "Dirac delta-function".

Operational Calculus and Generalized Functions

Operational Calculus and Generalized Functions Book
Author : Arthur Erdélyi
Publisher : Unknown
Release : 1962
ISBN : 0987650XXX
File Size : 30,7 Mb
Language : En, Es, Fr and De

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Operational Calculus and Generalized Functions Book PDF/Epub Download

Problems after each chapter

Lectures on Mikusi ski s Theory of Operational Calculus and Generalized Functions

Lectures on Mikusi  ski s Theory of Operational Calculus and Generalized Functions Book
Author : Arthur Erdélyi
Publisher : Unknown
Release : 1959
ISBN : 0987650XXX
File Size : 30,8 Mb
Language : En, Es, Fr and De

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Lectures on Mikusi ski s Theory of Operational Calculus and Generalized Functions Book PDF/Epub Download

Download Lectures on Mikusi ski s Theory of Operational Calculus and Generalized Functions book written by Arthur Erdélyi and published by with total hardcover pages 274 . Available in PDF, EPUB, and Kindle, read book directly with any devices anywhere and anytime.

Operational Calculus and Related Topics

Operational Calculus and Related Topics Book
Author : A. P. Prudnikov,K.A. Skórnik
Publisher : CRC Press
Release : 2006-08-15
ISBN : 1420011499
File Size : 51,7 Mb
Language : En, Es, Fr and De

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Operational Calculus and Related Topics Book PDF/Epub Download

Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering. Operational Calculus and Related Topics highlights the classical methods and applications as well as the recent advan

Generalized Functions Convergence Structures and Their Applications

Generalized Functions  Convergence Structures  and Their Applications Book
Author : Bogoljub Stankovic
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461310555
File Size : 43,5 Mb
Language : En, Es, Fr and De

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Generalized Functions Convergence Structures and Their Applications Book PDF/Epub Download

This Proceedings consists of a collection of papers presented at the International Conference "Generalized functions, convergence structures and their applications" held from June 23-27, 1987 in Dubrovnik, Yugoslavia (GFCA-87): 71 participants from 21 countr~es from allover the world took part in the Conference. Proceedings reflects the work of the Conference. Plenary lectures of J. Burzyk, J. F. Colombeau, W. Gahler, H. Keiter, H. Komatsu, B. Stankovic, H. G. Tillman, V. S. Vladimirov provide an up-to-date account of the cur rent state of the subject. All these lectures, except H. G. Tillman's, are published in this volume. The published communications give the contemporary problems and achievements in the theory of generalized functions, in the theory of convergence structures and in their applications, specially in the theory of partial differential equations and in the mathematical physics. New approaches to the theory of generalized functions are presented, moti vated by concrete problems of applications. The presence of articles of experts in mathematical physics contributed to this aim. At the end of the volume one can find presented open problems which also point to further course of development in the theory of generalized functions and convergence structures. We are very grateful to Mr. Milan Manojlovic who typed these Proce edings with extreme skill and diligence and with inexhaustible patience.

Generalized Functions and Convergence

Generalized Functions and Convergence Book
Author : Piotr Antosik,Andrzej Kamiński
Publisher : World Scientific
Release : 1990-09-12
ISBN : 9814611719
File Size : 36,8 Mb
Language : En, Es, Fr and De

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Generalized Functions and Convergence Book PDF/Epub Download

The conference was devoted to the memory of the late Professor Jan Mikusinski. The proceedings is divided into three parts. The first one contains biographical materials and memoirs about Professor Mikusinski and his work. The second part is devoted to the theory of generalized functions and the third to convergence structures. Contents:On Uniform Convergence of the Inner Product of Sequences (P Antosik et al)Decompositions of F-spaces into spaces with Properties K, N or k (J Burzyk)Finite Integral Transforms for Non-Local Boundary Value Problems (I H Dimovski & R I Petrova) On the Neutrix Convolution Product xs * xλ+ (B Fisher)On the Wiener-Laguerre Transform of Generalized Functions (H J Glaeske)On Distributional Solutions of the Generalized Entropy Equation (A Kaminski)On a Representation of the Algebra o of Mikusinski Operators (C Klis)Semilinear Wave Equations with Rough Initial Data: Generalized Solutions (M Oberguggenberger)Prodigious Mystery of Genuine Analysis (D Przeworska-Rolewicz)Asymtotic Bounds for the Distributional Stieltjes Transforms (A Takaci)On Tensor Product and Convolution of Generalized Functions of Gelfand-Shilov Type (J Uryga)Multidimensional Tauberian Theorems for Distributions (V S Vladimirov et al)and others Readership: Mathematicians and mathematical physicists.

Methods of the Theory of Generalized Functions

Methods of the Theory of Generalized Functions Book
Author : V. S. Vladimirov
Publisher : CRC Press
Release : 2002-08-15
ISBN : 9780415273565
File Size : 31,5 Mb
Language : En, Es, Fr and De

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Methods of the Theory of Generalized Functions Book PDF/Epub Download

This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics Book
Author : F. Farassat
Publisher : Unknown
Release : 1994
ISBN : 0987650XXX
File Size : 44,5 Mb
Language : En, Es, Fr and De

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Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics Book PDF/Epub Download

Download Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics book written by F. Farassat and published by with total hardcover pages 60 . Available in PDF, EPUB, and Kindle, read book directly with any devices anywhere and anytime.

Operational Calculus

Operational Calculus Book
Author : Gregors Krabbe
Publisher : Springer Science & Business Media
Release : 2013-12-01
ISBN : 1461343925
File Size : 22,7 Mb
Language : En, Es, Fr and De

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Operational Calculus Book PDF/Epub Download

Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable sub stitute for HEAVISIDE's operational calculus*. However, the Laplace transform procedure is unsatisfactory from several viewpoints (some of these will be mentioned in this preface); the most obvious defect: the procedure cannot be applied to functions of rapid growth (such as the 2 function tr-+-exp(t)). In 1949 JAN MIKUSINSKI indicated how the un necessary restrictions required by the Laplace transform can be avoided by a direct approach, thereby gaining in notational as well as conceptual simplicity; this approach is carefully described in MIKUSINSKI's textbook "Operational Calculus" [M 1]. The aims of the present book are the same as MIKUSINSKI's [M 1]: a direct approach requiring no un-necessary restrictions. The present operational calculus is essentially equivalent to the "calcul symbolique" of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook "Theorie des distributions" by LAURENT SCHWARTZ).

Generalized Functions and Operational Calculus

Generalized Functions and Operational Calculus Book
Author : I. Dimovski
Publisher : Unknown
Release : 1979
ISBN : 0987650XXX
File Size : 38,6 Mb
Language : En, Es, Fr and De

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Generalized Functions and Operational Calculus Book PDF/Epub Download

Download Generalized Functions and Operational Calculus book written by I. Dimovski and published by with total hardcover pages 216 . Available in PDF, EPUB, and Kindle, read book directly with any devices anywhere and anytime.

Introduction To The Operational Calculus

Introduction To The Operational Calculus Book
Author : Lothar Berg
Publisher : Elsevier
Release : 2013-07-19
ISBN : 0323162452
File Size : 25,6 Mb
Language : En, Es, Fr and De

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Introduction To The Operational Calculus Book PDF/Epub Download

Introduction to the Operational Calculus is a translation of "Einfuhrung in die Operatorenrechnung, Second Edition." This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work "Operational Calculus." Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant coefficients. In using operational calculus to solve more complicated problems than those of ordinary differential equations with constant coefficients, the concept of convergence assumes a significant role in the field of operators. This book also extends the Laplace transformation and applies it to non-transformable functions. This text also present three methods in which operational calculus can be modified and become useful in solving specific ranges of problems. These methods pertain to the finite Laplace transformation, to partial differential equations, and to the Volterra integral equations and ordinary differential equations with variable coefficients. This book can prove valuable for mathematicians, students, and professor of calculus and advanced mathematics.

Operational Calculus

Operational Calculus Book
Author : Thomas K. Boehme
Publisher : Elsevier
Release : 2014-08-01
ISBN : 1483161455
File Size : 47,9 Mb
Language : En, Es, Fr and De

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Operational Calculus Book PDF/Epub Download

Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included. Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-homogeneous equations and applications of operational calculus to partial differential equations. The section section deals with the integral of an operational function and its applications, along with integral transformations. A definition of operators in terms of abstract algebra is then presented. Operators as generalized functions, power series of operators, and Laplace transform are also discussed. Formulas of the operational calculus and tables of functions round out the book. This monograph will be useful to engineers, who regard the operational calculus merely as a tool in their work, and readers who are interested in proofs of theorems and mathematical problems.

Generalized Fractional Calculus and Applications

Generalized Fractional Calculus and Applications Book
Author : Virginia S Kiryakova
Publisher : CRC Press
Release : 1993-12-27
ISBN : 9780582219779
File Size : 31,7 Mb
Language : En, Es, Fr and De

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Generalized Fractional Calculus and Applications Book PDF/Epub Download

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.

Distribution Theory and Transform Analysis

Distribution Theory and Transform Analysis Book
Author : A.H. Zemanian
Publisher : Courier Corporation
Release : 2011-11-30
ISBN : 0486151948
File Size : 44,9 Mb
Language : En, Es, Fr and De

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Distribution Theory and Transform Analysis Book PDF/Epub Download

Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

Integral Transforms of Generalized Functions and Their Applications

Integral Transforms of Generalized Functions and Their Applications Book
Author : Ram Shankar Pathak
Publisher : Routledge
Release : 2017-07-05
ISBN : 1351562681
File Size : 24,6 Mb
Language : En, Es, Fr and De

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Integral Transforms of Generalized Functions and Their Applications Book PDF/Epub Download

For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.

Generalized Functions

Generalized Functions Book
Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
Release : 2011-06-27
ISBN : 0817681744
File Size : 51,8 Mb
Language : En, Es, Fr and De

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Generalized Functions Book PDF/Epub Download

Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises

Generalized Functions Volume 1

Generalized Functions  Volume 1 Book
Author : I. M. Gel′fand,G. E. Shilov
Publisher : American Mathematical Soc.
Release : 2016-04-19
ISBN : 1470426587
File Size : 45,7 Mb
Language : En, Es, Fr and De

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Generalized Functions Volume 1 Book PDF/Epub Download

he first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.

Integral Transforms and Operational Calculus

Integral Transforms and Operational Calculus Book
Author : H. M. Srivastava
Publisher : MDPI
Release : 2019-11-20
ISBN : 303921618X
File Size : 35,9 Mb
Language : En, Es, Fr and De

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Integral Transforms and Operational Calculus Book PDF/Epub Download

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications

Integral Transforms of Generalized Functions

Integral Transforms of Generalized Functions Book
Author : Brychkov
Publisher : CRC Press
Release : 1989-04-20
ISBN : 9782881247057
File Size : 22,7 Mb
Language : En, Es, Fr and De

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Integral Transforms of Generalized Functions Book PDF/Epub Download

English translation (from revised and enlarged versions of the Russian editions of 1977 and 1984) of a reference work which makes available to engineers, physicists and applied mathematicians theoretical and tabular material pertaining to certain extensions of standard integral transform techniques. Diverse transforms are touched upon, but the emphasis (particularly in the tables) is on generalized Fourier and Laplace transforms. Some multi-dimensional results are presented. Expensive, but nicely produced, and redundant with nothing standard to the reference shelves of mathematical libraries. (NW) Annotation copyrighted by Book News, Inc., Portland, OR