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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.
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This note was uploaded on 08/25/2011 for the course MATH 7338 taught by Professor Heil during the Fall '09 term at Georgia Institute of Technology.

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