الفهرس 
Introduction and summaryOnly 14 pages are availabe for public view
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Abstract
It is known that the famous Junctional Hilbert space L/R),
1f (Rl (Soboleu space) contum. t th t are not entire (even not etemen 5 a
smooth in the space L2{RJ). The aim of the present thesis is to
introduce and study some Hilbert spaces consisting oj entire
functions. The second aim of the thesis is to study the Fourier
transformation as an operator by which it is possible to define entire
junctions. For satisfying these aims it was necessary to present some
elementary ideas and concepts on analytic functions of a complex
variable, generalized function and some fundamental theorems from
the theory of real analysis.
The thesis consists of five sections.
The first section. Smooth and Analytic Fun.ctiDns oj a complex
or Real Variable. deals with analytic jUnctions of a complex vartable.
analytic junctions oj a real variable. and the test space and test
functions in one dimension.
The second section, Generalized Functions. deals with: The
’.
space of generalized functions in one dimension, and derivatives of
generalized function.
The third section. Hilbert Spaces and Fourier Tronsformations.
deals with : Abstract Hilbert spaces, Sobolev spaces. and the Fourier
transformation in L2(R).
Introduction anti Summary
The fourth section, Hilbert Spaces oj Entire Functions, deals
with: Some theorems oj Paley and Wiener, Paley-Wiener spaces, a
modified Paley-Wiener theorem. and modified Paley-Wiener spaces.
The fifth section, Characterization oj Fourier Transformations.
deals with : A characterization oj Fourier transformation in LiR}, and
a characterization of Fourier transformation in L2(R”J .