Analytic Fourier transforms and exponential approximations. I. (Russian) Zbl 1085.42005

Sedletskii, A. M.

Sovrem. Mat., Fundam. Napravl. 5, 3-152 (2003); translation in J. Math. Sci., New York 129, No. 6, 4251-4408 (2002).

This is the first part of a monograph presenting the authors’ results in harmonic analysis of functions of a real variable. Among the topics considered are:
a) distributions of zeroes of Fourier and Laplace transforms for compactly supported functions or measures;
b) completeness and minimality of systems \(\{\exp\{\lambda_n t\}:\lambda_n\in \Lambda\subset\mathbb{C}\}\);
c) nonharmonic Fourier series.
[See also the review of Part II in Zbl 1085.42006].

Reviewer: Yuri A. Brudnyi (Haifa)

MSC:

42A38	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A65	Completeness of sets of functions in one variable harmonic analysis
42C30	Completeness of sets of functions in nontrigonometric harmonic analysis
41A58	Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
44A10	Laplace transform

Keywords:

Fourier transform; Laplace transform; analyticity; nonharmonic Fourier series; completeness; minimality