An Introduction to Frames and Riesz Bases

ویرایش: 2 
نویسندگان: Ole Christensen (auth.)  
سری: Applied and Numerical Harmonic Analysis 
ISBN (شابک) : 9783319256115, 9783319256139 
ناشر: Birkhäuser Basel 
سال نشر: 2016 
تعداد صفحات: 719 
زبان: English 
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 9 مگابایت 

قیمت کتاب (تومان) : 39,000

This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field.

Key features include:

*Elementary introduction to frame theory in finite-dimensional spaces
* Basic results presented in an accessible way for both pure and applied mathematicians
* Extensive exercises make the work suitable as a textbook for use in graduate courses
* Full proofs includ

ed in introductory chapters; only basic knowledge of functional analysis required
* Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems

* Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory

* Selected research topics presented with recommendations for more advanced topics and further readin

g

* Open problems to stimulate further research

An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference.

Review of the first edition:

"Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field … . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research."

— Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005

Front Matter....Pages i-xxv
Frames in Finite-Dimensional Inner Product Spaces....Pages 1-46
Infinite-Dimensional Vector Spaces and Sequences....Pages 47-66
Bases....Pages 67-108
Bases and Their Limitations....Pages 109-118
Frames in Hilbert Spaces....Pages 119-151
Tight Frames and Dual Frame Pairs....Pages 153-164
Frames Versus Riesz Bases....Pages 165-181
Selected Topics in Frame Theory....Pages 183-198
Frames of Translates....Pages 199-240
Gabor Frames and Duality....Pages 241-256
Selected Topics on Gabor Frames....Pages 257-286
Frame Multiresolution Analysis....Pages 287-325
Wavelet Frames via Extension Principles....Pages 327-357
Selected Topics on Wavelet Frames....Pages 359-384
Frames on Locally Compact Abelian Groups....Pages 385-405
Perturbation of Frames....Pages 407-415
Approximation of the Inverse Frame Operator....Pages 417-444
Expansions in Banach Spaces....Pages 445-478
Back Matter....Pages 479-492
....Pages 493-517