Functions with Disconnected Spectrum Sampling, Interpolation, Translates

Olevskii, Alexander M./ Ulanovskii, Alexander

ISBN 10: 147042889X / ISBN 13: 9781470428891

Published by Amer Mathematical Society, 2016

About this Item

1st edition. 143 pages. 10.00x7.00x0.25 inches. In Stock.

Seller Inventory # __147042889X

Bibliographic Details

• Title: Functions with Disconnected Spectrum Sampling, Interpolation, Translates
• Publisher: Amer Mathematical Society
• Publication Date: 2016
• Language: English
• ISBN 10: 147042889X
• ISBN 13: 9781470428891
• Binding: Paperback
• Condition: Brand New
• Weight: 0.28 kilograms

About this title

Synopsis

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.

About the Author

Alexander M. Olevskii, Tel Aviv University, Israel. Alexander Ulanovskii, Stavanger University, Norway.