Author : Norman Levinson
Publisher : American Mathematical Soc.
ISBN 13 : 082181026X
Total Pages : 256 pages
Book Rating : 4.8/5 (218 download)
Book Synopsis Gap and Density Theorems by : Norman Levinson
Download or read book Gap and Density Theorems written by Norman Levinson and published by American Mathematical Soc.. This book was released on 1940-12-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.