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Abstract Harmonic Analysis: Volume I: Structure of Topological Groups Integration Theory Group Representations (Grundlehren der mathematischen Wissenschaften, 115)

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Abstract Harmonic Analysis: Volume I: Structure of Topological Groups Integration Theory Group Representations (Grundlehren der mathematischen Wissenschaften, 115)

4.85 18,320 ratings · 5,659 reviews
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Overview: When we acce pted th ekindinvitationof Prof. Dr. F. K. Scnxmrrto write a monographon abstract harmonic analysis for the Grundlehren. der Maihemaiischen Wissenscha/ten series, weintendedto writeall that wecouldfindoutaboutthesubjectin a textof about 600printedpages. We intended thatour book should be accessi ble tobeginners, and we hoped to makeit usefulto specialists as well. These aims proved to be mutually inconsistent. Hencethe presentvolume comprises onl y half of theprojectedwork. Itgives all ofthe structure oftopological groups neededfor harmonic analysisas it is known to u s; it treats integration on locallycompact groups in detail;it contains an introductionto the theory of group representati ons. In the second volume we will treat harmonicanalysisoncompactgroupsand locallycompactAbeliangroups, in considerable et d ail. Thebook is basedon courses given by E. HEWITT at the University of Washington and the University of Uppsala, althoughnaturallythe material of these courses has been en ormously expanded to meet the needsof a formal monograph. Like the. other treatments of harmonic analysisthathaveappeared since 1940, the book is a linealdescendant of A. WEIL'S fundamentaltreatise (WElL [4J)1. The debtof all workers in the field to WEIL'S work is wellknown and enormous. We havealso borrowed freely from LOOMIS'S treatmentof the subject (Lool\IIS[2 J), from NAIMARK [1J, and most especially from PONTRYA GIN [7]. In our exposition ofthestructur e of locally compact Abelian groups and of the PONTRYA GIN-VA N KAM PEN dualitytheorem, wehave beenstrongly influenced byPONTRYA GIN'S treatment. We hope to havejustified the writing of yet anothertreatiseon abstractharmonicanalysis by taking up recentwork, by writingoutthedetailsofeveryimportantconstruction andtheorem, andby including a largenumberof concrete ex amplesand factsnotavailablein other textbooks.

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Published January 1, 1963
ISBN 8137968
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Edwin Hewitt writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Edwin Hewitt lives with their spouse and a very vocal rescue cat.

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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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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Donald Wright
Donald Wright October 22, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Jessica King
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Sarah Brown
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
David Nelson
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Anthony Thomas
Anthony Thomas June 07, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Steven Campbell
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Andrew Green
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Rebecca Campbell
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Andrew Clark
Andrew Clark February 23, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Laura Evans
Laura Evans April 30, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Sandra Nguyen
Sandra Nguyen December 28, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Margaret Wilson
Margaret Wilson March 10, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
David Baker
David Baker October 01, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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David Baker March 01, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Daniel Lee
Daniel Lee June 24, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Sarah Nelson
Sarah Nelson September 20, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Richard Sanchez
Richard Sanchez August 26, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Charles Gomez
Charles Gomez April 20, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Michael Carter
Michael Carter August 06, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
George Robinson
George Robinson November 21, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Edward Turner
Edward Turner July 11, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Michael  Davis
Michael Davis November 04, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Anthony Campbell
Anthony Campbell December 12, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Ryan Jackson
Ryan Jackson March 29, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Patricia Lopez
Patricia Lopez February 02, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Kenneth Hill
Kenneth Hill March 05, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Melissa Gomez
Melissa Gomez August 04, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Kimberly Wilson
Kimberly Wilson March 10, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Sandra Perez
Sandra Perez August 31, 2025
It was adequate. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time.
Anthony Turner
Anthony Turner May 10, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Mark Moore
Mark Moore May 18, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Nancy Gonzalez
Nancy Gonzalez July 28, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Kenneth Thompson
Kenneth Thompson May 03, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Donald Thompson
Donald Thompson April 04, 2024
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Karen Wright
Karen Wright November 25, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Kenneth Hill
Kenneth Hill December 25, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Anthony Wilson
Anthony Wilson November 08, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
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