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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 55,629 ratings · 5,820 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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ISBN
8137968
Publication date
January 1, 1963
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Exceeded all my expectations. 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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I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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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.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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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.
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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.
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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.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Carol  Parker
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Christopher Jones
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A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
David Jackson
David Jackson January 09, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Rebecca Brown
Rebecca Brown August 03, 2024
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.
Laura Evans
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Kimberly Phillips
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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.
Joshua Thomas
Joshua Thomas September 08, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
James Cruz
James Cruz May 09, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Sharon King
Sharon King June 20, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Donald Hall
Donald Hall April 25, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Mark Rodriguez
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Steven Garcia
Steven Garcia June 07, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Dorothy Moore
Dorothy Moore March 23, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Betty Torres
Betty Torres December 19, 2024
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Sandra Hill
Sandra Hill March 12, 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.
Edward Edwards
Edward Edwards January 25, 2025
A decent, if standard, experience. 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 Carter
Cynthia Carter January 17, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Karen Baker
Karen Baker March 16, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Joseph Lopez
Joseph Lopez December 26, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Susan Gomez
Susan Gomez March 10, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Ashley Jackson
Ashley Jackson September 07, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Elizabeth Baker
Elizabeth Baker March 15, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Robert Rivera
Robert Rivera January 28, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Amanda Edwards
Amanda Edwards November 15, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Ashley  Davis
Ashley Davis March 11, 2024
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Gary Moore
Gary Moore April 10, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Paul Rodriguez
Paul Rodriguez June 30, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Amanda Lewis
Amanda Lewis August 16, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Robert Taylor
Robert Taylor May 15, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Eric Thompson
Eric Thompson November 08, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Rebecca Phillips
Rebecca Phillips April 13, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Jessica Carter
Jessica Carter January 01, 2024
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
David Jackson
David Jackson April 27, 2025
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.
Paul Martinez
Paul Martinez March 31, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Karen Turner
Karen Turner December 30, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Andrew Smith
Andrew Smith August 21, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Thomas Carter
Thomas Carter April 26, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Michelle Nelson
Michelle Nelson February 06, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Lisa Moore
Lisa Moore September 03, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Nicholas Adams
Nicholas Adams February 04, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
George Ramirez
George Ramirez April 22, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
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