Functions with Disconnected Spectrum: Sampling, Interpolation, Translates - Couverture souple

Olevskii, Alexander M.; Ulanovskii, Alexander

Couverture souple

ISBN 10 : 147042889X ISBN 13 : 9781470428891

Editeur : American Mathematical Society, 2016

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.

A propos du livre

À propos de l'auteur

Alexander M. Olevskii, Tel Aviv University, Israel.

Alexander Ulanovskii, Stavanger University, Norway.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 147042889X
• ISBN 13: 9781470428891
• Reliure: Broché
• Numéro d'édition: 1
• Nombre de pages: 143
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible