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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics, 100)

Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics)

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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics, 100)

Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions (Graduate Texts in Mathematics)

4.85 24,427 ratings · 2,600 reviews
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Overview: The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk� is positive definite for all finite choices of elements St, . . ., Sn from S. The three basic results mentioned above correspond to (, +, x* = -x), ([0, 00[, ], x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono- tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.

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Published June 6, 1984
ISBN 2709208
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After spending years working in the corporate world, Christian Berg finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Mark Brown
Mark Brown May 07, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Nancy Edwards
Nancy Edwards March 23, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
William Diaz
William Diaz August 10, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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Matthew Jackson August 30, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Joshua Torres June 15, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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David Sanchez December 22, 2025
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Betty Scott March 31, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Dorothy Mitchell May 23, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Robert Roberts March 10, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Eric Perez May 06, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Daniel Sanchez
Daniel Sanchez June 28, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Eric Adams
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Stephanie Turner May 04, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Stephanie Turner
Stephanie Turner February 22, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Christopher  Parker
Christopher Parker May 10, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Linda Ramirez
Linda Ramirez October 17, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Jennifer Martinez
Jennifer Martinez March 15, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Donald Edwards
Donald Edwards April 07, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Christopher  Parker
Christopher Parker March 15, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Melissa Campbell
Melissa Campbell October 17, 2024
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Joshua Hall
Joshua Hall June 24, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Christopher Walker
Christopher Walker November 01, 2024
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Cynthia Thomas
Cynthia Thomas August 14, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
William Martin
William Martin December 13, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Donna Hernandez
Donna Hernandez April 21, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Margaret Lewis
Margaret Lewis December 02, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
George Rivera
George Rivera August 14, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Paul Anderson
Paul Anderson April 04, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Michelle Williams
Michelle Williams March 05, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Andrew Turner
Andrew Turner November 07, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Melissa Torres
Melissa Torres March 23, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Richard Rivera
Richard Rivera October 22, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Kimberly Hall
Kimberly Hall July 28, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Christopher Turner
Christopher Turner July 06, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Lisa Reyes
Lisa Reyes June 10, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Eric Gomez
Eric Gomez December 13, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Kenneth Anderson
Kenneth Anderson June 20, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Joseph Robinson
Joseph Robinson November 07, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Carol Williams
Carol Williams October 04, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Betty Diaz
Betty Diaz December 02, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Donna Green
Donna Green July 07, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Karen Hall
Karen Hall January 05, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Nicholas Roberts
Nicholas Roberts March 04, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Laura Martinez
Laura Martinez November 12, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
George Jones
George Jones November 02, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Daniel Thompson
Daniel Thompson September 23, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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