Interpolation and Sampling in Spaces of Analytic Functions (University Lecture Series) - Tapa blanda

American Mathematical Society

 
9780821835548: Interpolation and Sampling in Spaces of Analytic Functions (University Lecture Series)
Tapa blanda
ISBN 10: 0821835548 ISBN 13: 9780821835548
Editorial: American Mathematical Society, 2004

Sinopsis

This book contains the latest developments in a central theme of research on analysis of one complex variable. The material is based on lectures at the University of Michigan. The exposition is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for $H^\infty$, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem.The author clarifies how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szego condition. Seip writes in a relaxed and fairly informal style, successfully blending informal explanations with technical details. The result is a very readable account of this complex topic. Prerequisites are a basic knowledge of complex and functional analysis. Beyond that, readers should have some familiarity with the basics of $H^p$ theory and BMO.

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

Reseña del editor

This book contains the latest developments in a central theme of research on analysis of one complex variable. The material is based on lectures at the University of Michigan. The exposition is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for $Hinfty$, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem. The author clarifies how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szego condition. Seip writes in a relaxed and fairly informal style, successfully blending informal explanations with technical details. The result is a very readable account of this complex topic. Prerequisites are a basic knowledge of complex and functional analysis. Beyond that, readers should have some familiarity with the basics of $Hp$ theory and BMO.

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

Editorial
American Mathematical Society
Año de publicación
2004
Idioma
Inglés
ISBN 10 
0821835548
ISBN 13 
9780821835548
Encuadernación
Tapa blanda
Número de páginas
139
Contacto del fabricante
no disponible
Persona responsable
no disponible