Distributions, Complex Variables, and Fourier Transforms
Author: Hans Bremermann
Publisher:
Published: 1965
Total Pages: 208
ISBN-13:
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Author: Hans Bremermann
Publisher:
Published: 1965
Total Pages: 208
ISBN-13:
DOWNLOAD EBOOKAuthor: James A. Hummel
Publisher:
Published: 1965
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Robert S Strichartz
Publisher: World Scientific Publishing Company
Published: 2003-06-13
Total Pages: 238
ISBN-13: 9813102292
DOWNLOAD EBOOKThis 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: Thomas Schucker
Publisher: World Scientific Publishing Company
Published: 1991-04-22
Total Pages: 182
ISBN-13: 9813104406
DOWNLOAD EBOOKIn 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:
Published: 1965
Total Pages: 210
ISBN-13:
DOWNLOAD EBOOKAuthor: Steven G. Krantz
Publisher: CRC Press
Published: 2019-04-16
Total Pages: 252
ISBN-13: 1000007189
DOWNLOAD EBOOKThe idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.
Author: Leon Ehrenpreis
Publisher: Courier Corporation
Published: 2011-11-30
Total Pages: 532
ISBN-13: 0486153037
DOWNLOAD EBOOKSuitable 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
Published: 2011-11-30
Total Pages: 404
ISBN-13: 0486151948
DOWNLOAD EBOOKDistribution 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: Hans Bremermann
Publisher:
Published: 1965
Total Pages: 186
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher: Academic Press
Published: 2014-05-14
Total Pages: 327
ISBN-13: 0080873448
DOWNLOAD EBOOKDistributions and Fourier Transforms