Gap and Density Theorems

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Mathematics - Analysis
Gap and Density Theorems

Gap and Density Theorems

Norman Levinson

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A typical gap theorem of the type discussed in the book deals with a set of exponential functions ${ \{e^{{{i\lambda}_n} x}\} }$ on an interval of the real line and explores the conditions under which this set generates the entire $L_2$ space on this interval. A typical gap theorem deals with functions $f$ on the real line such that many Fourier coefficients of $f$ vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various properties of zeros of analytic functions in one variable.

Категории:

Mathematics - Analysis

Год:

1940

Издательство:

American Mathematical Soc.

Язык:

english

Страницы:

256

ISBN 10:

082181026X