Distributions, Complex Variables, and Fourier Transforms PDF Download
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Author: Hans Bremermann
Publisher:
ISBN:
Category : Fourier transformations
Languages : en
Pages : 210
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Book Description
Author: Hans Bremermann
Publisher:
ISBN:
Category : Fourier transformations
Languages : en
Pages : 210
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Book Description
Author: James A. Hummel
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Robert S Strichartz
Publisher: World Scientific Publishing Company
ISBN: 9813102292
Category : Mathematics
Languages : en
Pages : 238
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Book Description
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Author: Schucker Thomas
Publisher: World Scientific Publishing Company
ISBN: 9813104406
Category : Science
Languages : en
Pages : 180
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Book Description
In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues:The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.
Author: Hans Bremermann
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Bernard W. Roos
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 552
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Book Description
Analytic functions -- Fourier transforms, causality, and dispersion relations -- The Wiener-Hopf technique -- Boundary value problems for sectionally analytic functions -- Distributions -- Applications in neutron transport theory -- Applications in plasma physics -- Appendix A. Paths, contours, and regions in the complex plane -- Appendix B. Order relations.
Author: Takahiro Kawai
Publisher: World Scientific
ISBN: 9812381619
Category : Mathematics
Languages : en
Pages : 339
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Book Description
This book is a collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics. Most of the papers originate from the talks given at the conference ?Prospects of Generalized Functions? (in November, 2001 at RIMS, Kyoto). Reflecting the fact that the papers, except M Morimoto's one, are dedicated to Mitsuo Morimoto, the subjects considered in this book are interdisciplinary, just as Morimoto's works are. The historical backgrounds of the subjects are also discussed in depth in some contributions. Thus, this book should be valuable not only to the specialists in the fields, but also to those who are interested in the history of modern mathematics such as distributions and hyperfunctions.
Author: Leon Ehrenpreis
Publisher: Courier Corporation
ISBN: 0486153037
Category : Mathematics
Languages : en
Pages : 532
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Book Description
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
Author: A.H. Zemanian
Publisher: Courier Corporation
ISBN: 0486151948
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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.
Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1420010956
Category : Mathematics
Languages : en
Pages : 443
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Book Description
From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, MapleTM, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences.
