Functions with Disconnected Spectrum: Sampling, Interpolation, Translates (University Lecture Series) - Tapa blanda

Olevskii, Alexander M.; Ulanovskii, Alexander

 
9781470428891: Functions with Disconnected Spectrum: Sampling, Interpolation, Translates (University Lecture Series)
Tapa blanda
ISBN 10: 147042889X ISBN 13: 9781470428891
Editorial: American Mathematical Society, 2016

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Alexander M. Olevskii, Tel Aviv University, Israel.

Alexander Ulanovskii, Stavanger University, Norway.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2016
Idioma
Inglés
ISBN 10 
147042889X
ISBN 13 
9781470428891
Encuadernación
Tapa blanda
Número de edición
1
Número de páginas
143
Contacto del fabricante
no disponible
Persona responsable
no disponible