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Author : Aurel Wintner
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (89 download)
Download or read book The Fourier Transforms of Probability Distributions written by Aurel Wintner and published by . This book was released on 1947 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fritz Oberhettinger
Publisher : Academic Press
ISBN 13 : 148321902X
Total Pages : 180 pages
Book Rating : 4.4/5 (832 download)
Download or read book Fourier Transforms of Distributions and Their Inverses written by Fritz Oberhettinger and published by Academic Press. This book was released on 2014-07-03 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.
Author : Tatsuo Kawata
Publisher : Academic Press
ISBN 13 : 148321852X
Total Pages : 681 pages
Book Rating : 4.4/5 (832 download)
Download or read book Fourier Analysis in Probability Theory written by Tatsuo Kawata and published by Academic Press. This book was released on 2014-06-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.
Author : William Fulton Dickenson
Publisher :
ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.:/5 (256 download)
Download or read book Fourier Transforms and Probability Distributions written by William Fulton Dickenson and published by . This book was released on 1973 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fritz Oberhettinger
Publisher : Springer Science & Business Media
ISBN 13 : 3642743498
Total Pages : 261 pages
Book Rating : 4.6/5 (427 download)
Download or read book Tables of Fourier Transforms and Fourier Transforms of Distributions written by Fritz Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences.
Author : Schucker Thomas
Publisher : World Scientific Publishing Company
ISBN 13 : 9813104406
Total Pages : 180 pages
Book Rating : 4.8/5 (131 download)
Download or read book Distributions, Fourier Transforms And Some Of Their Applications To Physics written by Schucker Thomas and published by World Scientific Publishing Company. This book was released on 1991-04-22 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Robert S. Strichartz
Publisher : World Scientific
ISBN 13 : 9789812384300
Total Pages : 238 pages
Book Rating : 4.3/5 (843 download)
Download or read book A Guide to Distribution Theory and Fourier Transforms written by Robert S. Strichartz and published by World Scientific. This book was released on 2003 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Pierre Brémaud
Publisher : Springer
ISBN 13 : 3319095900
Total Pages : 396 pages
Book Rating : 4.3/5 (19 download)
Download or read book Fourier Analysis and Stochastic Processes written by Pierre Brémaud and published by Springer. This book was released on 2014-09-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study.
Author :
Publisher : Academic Press
ISBN 13 : 0080873448
Total Pages : 327 pages
Book Rating : 4.0/5 (88 download)
Download or read book Distributions and Fourier Transforms written by and published by Academic Press. This book was released on 2014-05-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and Fourier Transforms
Author : L. Beall
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book The Application of the Discrete Fast Fourier Transform (FFT) to the Convolution of Probability Distributions written by L. Beall and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I︠U︡riĭ Vladimirovich Linnik
Publisher :
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.3/5 (91 download)
Download or read book Decomposition of Probability Distributions written by I︠U︡riĭ Vladimirovich Linnik and published by . This book was released on 1964 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Walter C. Giffin
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.3/5 (91 download)
Download or read book Transform Techniques for Probability Modeling written by Walter C. Giffin and published by . This book was released on 1975 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander I. Saichev
Publisher : Birkhäuser
ISBN 13 : 3319925865
Total Pages : 413 pages
Book Rating : 4.3/5 (199 download)
Download or read book Distributions in the Physical and Engineering Sciences, Volume 3 written by Alexander I. Saichev and published by Birkhäuser. This book was released on 2018-08-03 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.
Author : Saloman Bochner
Publisher : Univ of California Press
ISBN 13 : 0520372530
Total Pages : 184 pages
Book Rating : 4.5/5 (23 download)
Download or read book Harmonic Analysis and the Theory of Probability written by Saloman Bochner and published by Univ of California Press. This book was released on 2022-08-19 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Author : David W. Kammler
Publisher : Cambridge University Press
ISBN 13 : 1139469037
Total Pages : 39 pages
Book Rating : 4.1/5 (394 download)
Download or read book A First Course in Fourier Analysis written by David W. Kammler and published by Cambridge University Press. This book was released on 2008-01-17 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
Author : Hans Bremermann
Publisher :
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.F/5 ( download)
Download or read book Distributions, Complex Variables, and Fourier Transforms written by Hans Bremermann and published by . This book was released on 1965 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
ISBN 13 : 3642740294
Total Pages : 178 pages
Book Rating : 4.6/5 (427 download)
Download or read book Classical Fourier Transforms written by Komaravolu Chandrasekharan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a thorough introduction on classical Fourier transforms in a compact and self-contained form. Chapter I is devoted to the L1-theory: basic properties are proved as well as the Poisson summation formula, the central limit theorem and Wiener's general tauberian theorem. As an illustraiton of a Fourier transformation of a function not belonging to L1 (- , ) an integral due to Ramanujan is given. Chapter II is devoted to the L2-theory, including Plancherel's theorem, Heisenberg's inequality, the Paley-Wiener theorem, Hardy's interpolation formula and two inequalities due to Bernstein. Chapter III deals with Fourier-Stieltjes transforms. After the basic properties are explained, distribution functions, positive-definite functions and the uniqueness theorem of Offord are treated. The book is intended for undergraduate students and requires of them basic knowledge in real and complex analysis.
