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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 71,876 ratings · 3,684 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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Patricia Walker March 20, 2024
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Sharon King
Sharon King February 12, 2024
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Margaret Diaz
Margaret Diaz January 21, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Richard Reyes
Richard Reyes September 01, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Carol Moore
Carol Moore May 26, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Edward Robinson
Edward Robinson September 06, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Richard Hall
Richard Hall March 08, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Patricia Diaz
Patricia Diaz October 31, 2024
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.
Michael King
Michael King October 30, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Anthony Collins
Anthony Collins July 02, 2024
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Nicholas Turner
Nicholas Turner December 09, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Sharon Brown
Sharon Brown May 23, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Mary  Parker
Mary Parker July 17, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Richard Nelson
Richard Nelson November 01, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Linda Diaz
Linda Diaz October 19, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Kenneth Gonzalez
Kenneth Gonzalez July 12, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Deborah Hall
Deborah Hall November 15, 2025
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.
Michelle Wright
Michelle Wright September 05, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Kimberly Jones
Kimberly Jones March 21, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Donna Moore
Donna Moore October 18, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Patricia Hill
Patricia Hill July 23, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Mary Green
Mary Green July 05, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Kenneth Gonzalez
Kenneth Gonzalez March 26, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Andrew Miller
Andrew Miller March 01, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Gary Taylor
Gary Taylor July 26, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Margaret Sanchez
Margaret Sanchez March 11, 2025
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.
Emily Garcia
Emily Garcia March 27, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Jessica Reyes
Jessica Reyes September 29, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Nancy Mitchell
Nancy Mitchell January 27, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Jennifer Brown
Jennifer Brown November 06, 2025
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.
Emily Nguyen
Emily Nguyen February 29, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Melissa Gomez
Melissa Gomez July 06, 2024
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.
David Sanchez
David Sanchez February 28, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Paul Baker
Paul Baker March 16, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
George Perez
George Perez February 07, 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.
Amanda Walker
Amanda Walker September 06, 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. Quite impressive overall.
Jessica Wright
Jessica Wright July 23, 2024
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.
Donald Garcia
Donald Garcia February 20, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Sandra White
Sandra White November 16, 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. A solid 4 stars from me.
Jessica Smith
Jessica Smith January 22, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Nicholas Wright
Nicholas Wright February 06, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Jessica White
Jessica White November 14, 2024
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
Kimberly Lewis
Kimberly Lewis November 27, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Mary Brown
Mary Brown February 23, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Joshua Miller
Joshua Miller July 02, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Jacob Diaz
Jacob Diaz June 08, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Sharon Wilson
Sharon Wilson August 30, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Sandra Robinson
Sandra Robinson September 19, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Stephanie Williams
Stephanie Williams December 04, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
William Nguyen
William Nguyen December 23, 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.