Harmonic Analysis and the Theory of Probability

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Harmonic Analysis and the Theory of Probability by Salomon Bochner, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Salomon Bochner ISBN: 9780486154800
Publisher: Dover Publications Publication: November 7, 2013
Imprint: Dover Publications Language: English
Author: Salomon Bochner
ISBN: 9780486154800
Publisher: Dover Publications
Publication: November 7, 2013
Imprint: Dover Publications
Language: English
Nineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis.
Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic processes and the interchange of stimuli between probability and analysis. Non-probabilistic topics include Fourier series and integrals in many variables; the Bochner integral; the transforms of Plancherel, Laplace, Poisson, and Mellin; applications to boundary value problems, to Dirichlet series, and to Bessel functions; and the theory of completely monotone functions.
The primary significance of this text lies in the last two chapters, which offer a systematic presentation of an original concept developed by the author and partly by LeCam: Bochner's characteristic functional, a Fourier transform on a Euclidean-like space of infinitely many dimensions. The characteristic functional plays a role in stochastic processes similar to its relationship with numerical random variables, and thus constitutes an important part of progress in the theory of stochastic processes.
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Nineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis.
Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic processes and the interchange of stimuli between probability and analysis. Non-probabilistic topics include Fourier series and integrals in many variables; the Bochner integral; the transforms of Plancherel, Laplace, Poisson, and Mellin; applications to boundary value problems, to Dirichlet series, and to Bessel functions; and the theory of completely monotone functions.
The primary significance of this text lies in the last two chapters, which offer a systematic presentation of an original concept developed by the author and partly by LeCam: Bochner's characteristic functional, a Fourier transform on a Euclidean-like space of infinitely many dimensions. The characteristic functional plays a role in stochastic processes similar to its relationship with numerical random variables, and thus constitutes an important part of progress in the theory of stochastic processes.

More books from Dover Publications

Cover of the book North American Indian Beadwork Designs by Salomon Bochner
Cover of the book A Long Trip to Teatime by Salomon Bochner
Cover of the book Far from the Madding Crowd by Salomon Bochner
Cover of the book The Republic by Salomon Bochner
Cover of the book Braiding and Knotting by Salomon Bochner
Cover of the book An Introduction to Mathematical Modeling by Salomon Bochner
Cover of the book 3,000 Decorative Patterns of the Ancient World by Salomon Bochner
Cover of the book Pictorial Encyclopedia of Historic Ornament by Salomon Bochner
Cover of the book Introduction to Modern Algebra and Matrix Theory by Salomon Bochner
Cover of the book Das Lied von der Erde in Full Score by Salomon Bochner
Cover of the book Eighty Drawings by Salomon Bochner
Cover of the book You Can Draw Horses by Salomon Bochner
Cover of the book A Guide to Feynman Diagrams in the Many-Body Problem by Salomon Bochner
Cover of the book Utilitarianism by Salomon Bochner
Cover of the book Quantitative Zoology by Salomon Bochner
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy