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This revised and expanded monograph presents a comprehensive theory for frames and Riesz bases in Hilbert spaces, along with practical applications in Gabor analysis, wavelet analysis, and generalized shift-invariant systems. The second edition emphasizes explicit constructions with appealing properties and includes new sections on LCA groups, generalized shift-invariant systems, and duality theory for Gabor and wavelet frames, reflecting a decade of advancements in frame theory. Key features include an elementary introduction to frame theory in finite-dimensional spaces, accessible basic results for both pure and applied mathematicians, and extensive exercises suitable for graduate courses. Full proofs are provided in introductory chapters, requiring only a basic understanding of functional analysis. The book discusses explicit constructions of frames and dual pairs, with applications to time-frequency analysis and connections to sampling theory. Selected research topics and recommendations for further reading are included, along with open problems to encourage continued research. This work will appeal to graduate students and researchers in pure and applied mathematics, mathematical physics, and engineering, as well as professionals in digital signal processing seeking to understand the underlying theory of modern tools.
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An Introduction to Frames and Riesz Bases, Ole Christensen
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- Année de publication
- 2018
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