Fourier Analysis In Probability Theory PDF Download
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Author | : Tatsuo Kawata |
Publisher | : Academic Press |
Total Pages | : 681 |
Release | : 2014-06-17 |
Genre | : Mathematics |
ISBN | : 148321852X |
Download Fourier Analysis in Probability Theory Book in PDF, ePub and Kindle
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 | : TATSUO. KAWATA |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : |
ISBN | : 9781033050385 |
Download FOURIER ANALYSIS IN PROBABILITY THEORY Book in PDF, ePub and Kindle
Author | : Salomon Bochner |
Publisher | : Courier Corporation |
Total Pages | : 190 |
Release | : 2013-11-07 |
Genre | : Mathematics |
ISBN | : 0486154807 |
Download Harmonic Analysis and the Theory of Probability Book in PDF, ePub and Kindle
Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.
Author | : Pierre Brémaud |
Publisher | : Springer |
Total Pages | : 396 |
Release | : 2014-09-16 |
Genre | : Mathematics |
ISBN | : 3319095900 |
Download Fourier Analysis and Stochastic Processes Book in PDF, ePub and Kindle
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 | : John J. Benedetto |
Publisher | : CRC Press |
Total Pages | : 668 |
Release | : 1995-09-21 |
Genre | : Mathematics |
ISBN | : 9780849315152 |
Download Journal of Fourier Analysis and Applications Special Issue Book in PDF, ePub and Kindle
At the end of June 1993, a Conference in Harmonic Analysis was held at the University of Paris-Sud to celebrate the role played by Jean-Pierre Kahane. The large variety of topics ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Kahane.
Author | : Saloman Bochner |
Publisher | : Univ of California Press |
Total Pages | : 184 |
Release | : 2022-08-19 |
Genre | : Mathematics |
ISBN | : 0520372530 |
Download Harmonic Analysis and the Theory of Probability Book in PDF, ePub and Kindle
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 | : Elias M. Stein |
Publisher | : Princeton University Press |
Total Pages | : 326 |
Release | : 2011-02-11 |
Genre | : Mathematics |
ISBN | : 1400831237 |
Download Fourier Analysis Book in PDF, ePub and Kindle
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Author | : Audrey Terras |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 1999-03-28 |
Genre | : Mathematics |
ISBN | : 9780521457187 |
Download Fourier Analysis on Finite Groups and Applications Book in PDF, ePub and Kindle
It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Author | : Mark A. Pinsky |
Publisher | : American Mathematical Soc. |
Total Pages | : 398 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 082184797X |
Download Introduction to Fourier Analysis and Wavelets Book in PDF, ePub and Kindle
This text provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. It contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
Author | : Herbert Heyer |
Publisher | : World Scientific |
Total Pages | : 425 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 9814282480 |
Download Structural Aspects in the Theory of Probability Book in PDF, ePub and Kindle
The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.