Sinossi
This volume contains 12 lectures on functions with disconnected spectrum, dealing with problems of Fourier analysis, which are partially inspired by signal theory. It discusses the classical sampling problem, the problem of interpolation of discrete functions by analytic ones with spectrum in S, and the problem of completeness of discrete translates. It provides an elementary introduction; classical results due to Beurling, Kahane, and Landau; recent progress in the area, such as construction of universal sampling sets and high-dimensional and non-analytic phenomena; and the completeness problem for discrete translates. It illustrates how methods of harmonic and complex analysis interact with various key concepts in different areas, such as Minkowski's lattice, Kolmogorov's width, Meter's quasicrystals, and others. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)
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Functions with Disconnected Spectrum: Sampling, Interpolation, Translates (University Lecture Series)
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American Mathematical Society, 2016
ISBN 10: 147042889X
ISBN 13: 9781470428891
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Condizione: New. Series: University Lecture Series. Num Pages: 143 pages. BIC Classification: PBK. Category: (G) General (US: Trade). Dimension: 254 x 178. . . 2016. 1st Edition. paperback. . . . . Codice articolo V9781470428891
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Functions with Disconnected Spectrum : Sampling, Interpolation, Translates
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Functions with Disconnected Spectrum
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American Mathematical Society, US, 2016
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Paperback. Condizione: New. 1st. The classical sampling problem is to reconstruct entire functions with given spectrum $S$ from their values on a discrete set $L$. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets $L$ the exponential system with frequencies in $L$ forms a frame in the space $L^2(S)$. The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in $S$ and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum $S$ and the discrete set $L$ play a crucial role in these problems.After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena.The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, such as Minkowski's lattice, Kolmogorov's width, and Meyer's quasicrystals.The book is addressed to graduate students and researchers interested in analysis and its applications. Due to its many exercises, mostly given with hints, the book could be useful for undergraduates. Codice articolo LU-9781470428891
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Functions with Disconnected Spectrum: Sampling, Interpolation, Translates (University Lecture Series)
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American Mathematical Society, 2016
ISBN 10: 147042889X
ISBN 13: 9781470428891
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Condizione: New. Series: University Lecture Series. Num Pages: 143 pages. BIC Classification: PBK. Category: (G) General (US: Trade). Dimension: 254 x 178. . . 2016. 1st Edition. paperback. . . . . Books ship from the US and Ireland. Codice articolo V9781470428891
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Functions with Disconnected Spectrum : Sampling, Interpolation, Translates
Editore:
American Mathematical Society, 2016
ISBN 10: 147042889X
ISBN 13: 9781470428891
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Functions with Disconnected Spectrum
Editore:
American Mathematical Society, US, 2016
ISBN 10: 147042889X
ISBN 13: 9781470428891
Nuovo
Paperback
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Da: Rarewaves.com UK, London, Regno Unito
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Paperback. Condizione: New. 1st. The classical sampling problem is to reconstruct entire functions with given spectrum $S$ from their values on a discrete set $L$. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets $L$ the exponential system with frequencies in $L$ forms a frame in the space $L^2(S)$. The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in $S$ and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum $S$ and the discrete set $L$ play a crucial role in these problems.After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena.The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, such as Minkowski's lattice, Kolmogorov's width, and Meyer's quasicrystals.The book is addressed to graduate students and researchers interested in analysis and its applications. Due to its many exercises, mostly given with hints, the book could be useful for undergraduates. Codice articolo LU-9781470428891
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Functions With Disconnected Spectrum: Sampling, Interpolation, Translates (University Lecture Series) (University Lecture Series, 65)
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