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Gap and density theorems

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...

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Detalles Bibliográficos
Autor principal: Levinson, N
Lenguaje:eng
Publicado: American Mathematical Society 1940
Materias:
Acceso en línea:http://cds.cern.ch/record/2264176
Descripción
Sumario: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 propertie