SOME RELEVANT AND NOT-SO-RELEVANT TEXTS
Christopher Heil
School of Mathematics, Georgia Tech
This is a sampling of some texts in subjects more-or-less related to the courses I usually teach, limited to books
that I happen to know and/or like.
1. Hilbert Space Theory
(1) L. Debnath and P. Mikusi´nski,
Introduction to Hilbert Spaces with Applications
, Second Edition, Academic
Press, 1999. This is the Hilbert space book I usually use as a textbook. It is fairly decently written but has
occasional annoying lapses.
(2) I. Gohberg and S. Goldberg,
Basic Operator Theory
, Birkh¨
auser, 2001 (reprint of the 1981 original).
A
nice, easy-to-read introduction to Hilbert space theory. The typeface is not very stylish, but don’t hold that
against it.
(3) E. Kreyszig,
Introductory Functional Analysis with Applications
, Wiley, 1978. Very nicely written, includes
a lot of Banach space stuF in addition to Hilbert spaces, which makes it a little di±cult to use as a textbook
but by the same token makes it an excellent supplement and reference.
(4) R. Young,
An Introduction to Nonharmonic Fourier Series
, Academic Press, 1980. The motivation for this
book is ²ourier series, not Hilbert spaces, so it should really go under the Harmonic Analysis section. However,
it is a very readable book, with lots of good information on bases and frames in Hilbert spaces, so it’s worth
keeping in mind as a Hilbert space reference.
2. Linear Algebra
(1) G. Strang,
Introduction to Linear Algebra
, Wellesley–Cambridge Press, 1993.
Lots of good, easy-to-read
information on ³nite-dimensional matrix theory. Gets you beyond mere mechanics of matrix operations.