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Harmonic Analysis and the Theory of ProbabilityNineteenth 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
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.
Binding Type: Paperback
Publisher: Dover Publications
Published: 08/27/2005
ISBN: 9780486446202
Pages: 176
Weight: 0.44lbs
Size: 8.46h x 5.52w x 0.39d
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★★★★★ 3
I don't understand the Hype.
Format: Paperback
Everyone seems to love Glannon but I found other E&Es to me much straightforward and easy to understand. Don't know what it is about Glannon's writing. Not terrible, just not conducive to me for whatever reason. Negligence sections were lacking.
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Reviewed in the United States on May 5, 2022
★★★★★ 1
Garbage. Order from a REAL bookstore or publisher
Format: Paperback
Book came cut off and assembled UPSIDE DOWN wtf is this?? Definitely demanding a refund. This is straight up GARBAGE should've just bought from b&n
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Reviewed in the United States on November 5, 2022
★★★★★ 1
Came used with dirty pages
Format: Paperback
The book clearly is not new, the pages are folded over and dirty with dirt. There is a sticky residue on the back cover of the book. Really gross.
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Reviewed in the United States on December 15, 2021
★★★★★ 5
Best E&E out there
Format: Paperback
This is the best E&E book out there! Helped me a ton in Torts and I owe my A in Torts to this book. There's a whole section on how to write a torts exam and the examples & explanation sections are AMAZING and really detailed. The best sections are on factual/actual cause and proximate cause and the nuances between the two.
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Reviewed in the United States on June 5, 2025
★★★★★ 5
Golden Book Baby Animals
Format: Hardcover
Love the book!!! ADORABLE!!!!!
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Reviewed in the United States on April 16, 2026
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