SKU: 21540695109

Harmonic Analysis and the Theory of Probability

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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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SKU: 21540695109

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STEPHEN SWENERTON
Bozeman, US
★★★★★ 5
EXCELLENT RESOURCE
Format: Hardcover
OUTSTANDING SUMMARY OF THE EVENTS LEADING UP TO THE CURRENT VERY UNFORTUNATE SITUATION. I USED IT AS MY PRIMARY SOURCE FOR A CLASS I AM TEACHING ON THE SUBJECT OF THE WAR IN IRAN.
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Reviewed in the United States on May 24, 2026
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Max
Chelsea, US
★★★★★ 5
an excellent reference book
Format: Hardcover
At a time when the U.S. and Israel’s military operation against Iran has become one of the most important issues on the global agenda, this is an excellent reference book that summarizes the historical development of events and provides valuable context for better understanding what is happening today.
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Reviewed in the United States on May 11, 2026
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Mr. Flex
Phoenix, US
★★★★★ 5
Great for better understanding Iran's strategic perspectives
Format: Hardcover
The book moves through the growth of Iran's strategic history since the 1979 revolution. By the time it gets to the last 100 pages its very interesting as far as understanding Iran's perspective. Also found it chilling how foreboding many parts were in light of what is happening right now
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Reviewed in the United States on March 2, 2026
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Hassan Nasir
Los Angeles, US
★★★★★ 5
Great book to understand Iran's strategy in a historical context
Nasr provides a solid understanding of Iran both in contemporary and historical context. It makes the case clear what and how Iran is thinking. Reading it at the time of Us-Israel and Iran war helped make sense of the news media, which often follows shallow analysis.
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Reviewed in the United States on March 27, 2026
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TJMjr
Massapequa, US
★★★★★ 5
Iran’s Strategic Error.
Format: Audiobook
Excellent discussion of Iran’s grand strategy in what they believe will protect their Nation as they continue as the world’s pariah. The book is well written and clearly lays out the history of Iran over the past 50-60 years and why they are implementing this strategy albeit a failed one, and the results. The Ayatollahs continue to pursue the destruction of Israel and struggle via terrorism and supporting war proxies to become the regions power, instead of pursuing economic wealth. This book describes the how’s and whys of this failed strategy. Good reading
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Reviewed in the United States on November 15, 2025

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