Based on a streamlined presentation of the author's successful work, An Introduction to Frames and Riesz Bases , this new textbook develops frame theory as part of a dialogue between mathematicians and engineers.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases , this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field.

Key features include results presented in a way that is accessible to graduate students, mathematicians, and engineers; a presentation of basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces; extensive exercises; and a detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames.

Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Fills a gap in the literature: develops frame theory as part of a dialogue between mathematicians and engineers Results are presented in a way that is accessible to graduate students in mathematics and engineering Extensive exercises are included May be used as a textbook in theoretical graduate courses on bases and frames or application-oriented courses focusing on either Gabor anlaysis or wavelets For a broad audience of graduate students and researchers in mathematics, mathematical physics, and engineering; also useful for practitioners working in digital signal processing Includes supplementary material: sn.pub/extras

Autorentext

Ole Christensen is a Professor at Technical University of Denmark in the Department of Applied Mathematics and Computer Science. His research interests include harmonic analysis, frame expansions, wavelets, and Gabor systems.

Klappentext

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Featuring extensive exercises, this book will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Inhalt
Frames in Finite-dimensional Inner Product Spaces.- Infinite-dimensional Vector Spaces and Sequences.- Bases.- Bases and their Limitations.- Frames in Hilbert Spaces.- B-splines.- Frames of Translates.- Shift-Invariant Systems.- Gabor Frames in L(R).- Gabor Frames in l(Z).- Wavelet Frames in L(R).