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For over three decades, this best-selling classic has been used by
thousands of students in the United States and abroad as a
must-have textbook for a transitional course from calculus to
analysis. It has proven to be very useful for mathematics majors
who have no previous experience with rigorous proofs. Its friendly
style unlocks the mystery of writing proofs, while carefully
examining the theoretical basis for calculus. Proofs are given in
full, and the large number of well-chosen examples and exercises
range from routine to challenging. The second edition preserves the
book's clear and concise style, illuminating discussions, and
simple, well-motivated proofs. New topics include material on the
irrationality of pi, the Baire category theorem, Newton's method
and the secant method, and continuous nowhere-differentiable
functions.
This book is a continuation of vol. I (Grundlehren vol. 115, also
available in softcover), and contains a detailed treatment of some
important parts of harmonic analysis on compact and locally compact
abelian groups. From the reviews: "This work aims at giving a
monographic presentation of abstract harmonic analysis, far more
complete and comprehensive than any book already existing on the
subject...in connection with every problem treated the book offers
a many-sided outlook and leads up to most modern developments.
Carefull attention is also given to the history of the subject, and
there is an extensive bibliography...the reviewer believes that for
many years to come this will remain the classical presentation of
abstract harmonic analysis." Publicationes Mathematicae
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.
Revised and updated second edition with new material Text for a
transition course between calculus and more advanced analysis
courses Contains new material on topics such as irrationality of
pi, the Baire category theorem, Newton's method and the secant
method, and continuous nowhere-differentiable functions Includes
new examples and improved proofs For over three decades, this
best-selling classic has been used by thousands of students in the
United States and abroad as a must- have textbook for a
transitional course from calculus to analysis. It has proven to be
very useful for mathematics majors who have no previous experience
with rigorous proofs. Its friendly style unlocks the mystery of
writing proofs, while carefully examining the theoretical basis for
calculus. Proofs are given in full, and the large number of
well-chosen examples and exercises range from routine to
challenging. The second edition preserves the book's clear and
concise style, illuminating discussions, and simple, well-motivated
proofs. New topics include material on the irrationality of pi, the
Baire category theorem, Newton's method and the secant method, and
continuous nowhere-differentiable functions.
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