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Paul Richard Halmos, who lived a life of unbounded devotion to
mathematics and to the mathematical community, died at the age of
90 on October 2, 2006. This volume is a memorial to Paul by
operator theorists he inspired. Paul'sinitial research,beginning
with his 1938Ph.D. thesis at the University of Illinois under
Joseph Doob, was in probability, ergodic theory, and measure
theory. A shift occurred in the 1950s when Paul's interest in
foundations led him to invent a subject he termed algebraic logic,
resulting in a succession of papers on that subject appearing
between 1954 and 1961, and the book Algebraic Logic, published in
1962. Paul's ?rst two papers in pure operator theory appeared in
1950. After 1960 Paul's research focused on Hilbert space
operators, a subject he viewed as enc- passing ?nite-dimensional
linear algebra. Beyond his research, Paul contributed to
mathematics and to its community in manifold ways: as a renowned
expositor, as an innovative teacher, as a tireless editor, and
through unstinting service to the American Mathematical Society and
to the Mathematical Association of America. Much of Paul's in?uence
?owed at a personal level. Paul had a genuine, uncalculating
interest in people; he developed an enormous number of friendships
over the years, both with mathematicians and with
nonmathematicians. Many of his mathematical friends, including the
editors
ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul'sknee,
learned from his advice and his example what it means to be a
mathematician.
Complex Function Theory is a concise and rigorous introduction to
the theory of functions of a complex variable. Written in a
classical style, it is in the spirit of the books by Ahlfors and by
Saks and Zygmund. Being designed for a one-semester course, it is
much shorter than many of the standard texts. Sarason covers the
basic material through Cauchy's theorem and applications, plus the
Riemann mapping theorem. It is suitable for either an introductory
graduate course or an undergraduate course for students with
adequate preparation. The first edition was published with the
title Notes on Complex Function Theory.
Spaces of holomorphic functions have been a prominent theme in
analysis since early in the twentieth century. Of interest to
complex analysts, functional analysts, operator theorists, and
systems theorists, their study is now flourishing. This volume, an
outgrowth of a 1995 program at the Mathematical Sciences Research
Institute, contains expository articles by program participants
describing the present state of the art. Here researchers and
graduate students will encounter Hardy spaces, Bergman spaces,
Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of
the role these objects play in modern analysis.
Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.
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