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Review of Steven Krantz's A Panorama of Harmonic Analysis

Summary: Review of Steven Krantz's A Panorama of
Harmonic Analysis
by J. Marshall Ash
Department of Mathematics, DePaul University, Chicago, IL 60614
March 17, 2000
I had some trouble with the topology section of the University of Chicago's
master of science exam in May 1963. But the analysis section went very well.
No small part of the credit for this was due to Antoni Zygmund who had taught
me real analysis I and II and to Alberto CalderŽon who had taught me complex
analysis I and II. In very short order, I abandoned my plan of specializing in
point set topology and picked Fourier series as the main topic for my next
hurdle, the two topic exam. Over the next year, Bill Connant, Larry Dornoff,
and I read Zygmund's Trigonometric Series in preparation for the exam. After
the exam, Professor Zygmund accepted me as his student and my career as a
harmonic analyst began.
Looking through Krantz's A Panorama of Harmonic Analysis feels like
watching a home video production entitled "The Zygmund School of Analy-
sis: 1965-1999." Throughout this period, I was lucky enough to be near the
University of Chicago, where the Monday 3:45 PM CalderŽon-Zygmund seminar
has featured, among many other things, just about every development in har-


Source: Ash, J. Marshall - Department of Mathematical Sciences, DePaul University


Collections: Mathematics