Frames and Time-Frequency Analysis
A very short survey on frames for general mathematical audiences:
WHAT IS a Frame?, C. Heil,
Notices Amer. Math. Soc., 60 (2013), 748-750.
A Basis Theory Primer,
C. Heil, Birkhauser, Boston (2011).
- Most of the lectures will be based on the material in
Chapters 7, 8 (Sections 8.1-8.4), and 11.
- Chapters 1 and 2 contain background on Banach and Hilbert spaces,
operator theory, and functional analysis.
- Chapter 9 contains a short review of the Fourier transform.
Errata List is available (and please notify the author if you find additional typos!)
- The original 1998 unexpanded version is available
However, that version covers only a limited portion of the material that
will be presented in the lectures.
An old survey paper that covers some of the material
on frames and Gabor frames (more concisely than the Basis Primer):
Continuous and discrete wavelet transforms,
C. E. Heil and D. F. Walnut,
SIAM Review, 31 (1989), 628-666.
A survey on Wiener amalgam spaces:
An introduction to weighted Wiener amalgams,
C. Heil, in: "Wavelets and their Applications",
M. Krishna, R. Radha and S. Thangavelu, eds.,
Allied Publishers, New Delhi (2003), 183-216.
Preliminary LECTURE NOTES (works in progress!).
Other Useful References:
An introduction to frames in finite dimensions:
Frames for Undergraduates,
D. Han, K. Kornelson, D. Larson, and E. Weber,
AMS, Providence, 2007.
The title says it all:
Foundations of Time-Frequency Analysis,
Birkhäuser, Boston (2001).
A very nice volume complementary to the Basis Primer:
An Introduction to Frames and Riesz Bases,
Birkhäuser, Boston (2003).