Gap and Denisty 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 $f$ 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...
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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.