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Description
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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4.2 ★★★★★
Based on 14 reviews
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Product Reviews
★★★★★ 5
Wonderful
Format: Kindle
What a wonderful long read, with depth, emotions, storyline and a touch of $mut. This story was definitely more centered around the storyline rather than any $ex scenes and lived up to “Cozy Omegaverse”. We saw the pack dynamic’s evolve as she was ready for them to evolve, they were patient with her and allowed her to break free from her own constraints.
Amazing!
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Reviewed in the United States on June 25, 2025
★★★★★ 4
A Nice Story
Format: Kindle
I love Omegaverse and its many stories. The book is a wonderful story. The characters are intriguing and are each unique. There were a few issues with repetitive phrases through out the book and a few misspellings but the biggest issue was the very painful slow burn. I feel if it weren’t so slow
It could have incorporated more content about each character. Overall a solid story though.
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Reviewed in the United States on April 25, 2025
★★★★★ 3
decent…but
Format: Kindle
This is my first book from this author, and while I do really love omegaverse stories, this one left a lot to be desired. This book is a hard-core slow, slow, slow burn: (75% or later in the book)
I will say that I finished it. Unfortunately, I struggled through a lot of it due to punctuation errors, and general editing that must have been looked over during the revision process.
I also feel like a lot of information was left out and there wasn’t closure regarding her parents. The dynamic of the pack before Lydia joined is a little confusing, the only person who showed affection towards Elias was the Head alpha. The other two seemed indifferent to him in an intimate relationship way. That doesn’t really scream cohesive pack to me.
I am hopeful that the next book in the series is better edited, and that the author decides not to use the same phrases over and over again. I’m pretty sure “honey-warm” was mentioned over 15 times when describing Elias’s scent. That got really old, really fast.
Overall, it was a decent book. Not sure I would read it again or recommend it until of these errors are remedied.
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Reviewed in the United States on April 26, 2025
★★★★★ 5
Definitely a comfort read
Format: Kindle
Just a comfy cozy nice long read. While this is definitely a SLOOOOOOOOWWWWW burn, this is how you do RH right; a nice long novel where you actually get to know the characters so you can feel more connected to them & the story, not to mention getting enough time to actually remember all their names haha. & they are all consent kings. Also I do so love me some double omega OV, siiiigh (heart eyes). I wish there had been juuust a bit more spice, like maybe just between Elias & others before MC was ready (made Elias feel a bit underdone or gimmicky without it), I did love this read. Low stress, comfy read. It could've used another round of editing for some minor errors & type issues but it wasn't bad enough to pull ne out of the story. Though I did giggle at 'knecks', thinking kuh-necks in my head. Overall I'd say 9/10
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Reviewed in the United States on March 28, 2025
★★★★★ 4
beautiful story
Format: Kindle
I absolutely love this book, however there is quite a bit repetition! The storyline makes up for it, a just skipped them. I like that this was a cozy read, it’s an omegaverse romance, but really barely read as OV, you get a little hierarchy and scent blockers, but if not for that you wouldn’t know. I love the romance aspect however, they take there time and move at her pace! A good read, with some errors, hopefully there is more to come!!
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Reviewed in the United States on April 13, 2025