Interpolation and Sampling in Spaces of Analytic Functions
Seip, Kristian,
Interpolation and Sampling in Spaces of Analytic Functions / Kristian Seip - Providence, Island : American Mathematical Society, ©2004. - xii, 139 pages : illustrations ; 25 cm. - University lecture series (Providence, R.I.), 33. .
Ch. 1. Carleson's interpolation theorem --
Ch. 2. Interpolating sequences and the Pick property --
Ch. 3. Interpolation and sampling in Bergman spaces --
Ch. 4. Interpolation in the Bloch space --
Ch. 5. Interpolation, sampling, and Toeplitz operators --
Ch. 6. Interpolation and sampling in Paley-Wiener spaces.
"The book 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[superscript [infinity]], and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem." "The book aims at clarifying 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." "The book is based on six lectures given by the author at the University of Michigan. This is reflected in the exposition, which is a blend of informal explanations with technical details." "The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiarity with the basic of H[superscript p] theory and BMO."--Jacket
9780821835548
Zafaa Books & Distributors ;313/56F 49A, Anand Nagar Inderlok Delhi 110035
Mathematics
Analysis
Analytic functions.
Hardy classes.
Generalized spaces.
Interpolation.
Classes de Hardy.
Analytische Funktion
Hardy-Klasse
515.9 SEL
Interpolation and Sampling in Spaces of Analytic Functions / Kristian Seip - Providence, Island : American Mathematical Society, ©2004. - xii, 139 pages : illustrations ; 25 cm. - University lecture series (Providence, R.I.), 33. .
Ch. 1. Carleson's interpolation theorem --
Ch. 2. Interpolating sequences and the Pick property --
Ch. 3. Interpolation and sampling in Bergman spaces --
Ch. 4. Interpolation in the Bloch space --
Ch. 5. Interpolation, sampling, and Toeplitz operators --
Ch. 6. Interpolation and sampling in Paley-Wiener spaces.
"The book 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[superscript [infinity]], and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem." "The book aims at clarifying 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." "The book is based on six lectures given by the author at the University of Michigan. This is reflected in the exposition, which is a blend of informal explanations with technical details." "The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiarity with the basic of H[superscript p] theory and BMO."--Jacket
9780821835548
Zafaa Books & Distributors ;313/56F 49A, Anand Nagar Inderlok Delhi 110035
Mathematics
Analysis
Analytic functions.
Hardy classes.
Generalized spaces.
Interpolation.
Classes de Hardy.
Analytische Funktion
Hardy-Klasse
515.9 SEL
