السلام عليكم ورحمة الله وبركاته
ما يلي عبارة عن الخلاصة لبحث ما جستير عن تحويل هلبرت
فلعلكم تجدون فيه ما يفيد.
Theses and Dissertations Abstracts Full Information
Title
Generalized Hilbert Transform with applications.
Author
Al-Saeed, Yousef Muhammad Ali
Department
Mathematical Sciences
Degree
Master of Science
Date Submitted
March 1988
Date Accepted
April 4, 1988
Collation
82 Leaves : ill. ; 28 cm.
Shelflist Number
A 1.S34
Committee Advisor
Chaudhry, M.A
Committee Members
. Lyzzaik, A. K.
Walker, Peter
English Abstract
The dissertation consists of three chapters. In Chapter 1, we define the classical Hilbert-transform, give conditions for its existence and discuss some of its important properties. We also discuss Hilbert formulae, a convolution theorem, an inversion formula, Parseval's relation, Fourier transforms of Hilbert transform and we consider the Hilbert transform as a convolution operator. In the last of this chapter, we give applications to some integral equations. In Chapter 2, we shall give a general introduction to the theory of countable normed spaces and discuss some general results of compatibility of norms, linear topological spaces and completeness of the spaces. The convergence and completeness criteria for the conjugate space shall be discussed as well. In Chapter 3, the classical Hilbert-transform is proved to be a homeomorphism from the test space DLp (IR) (l = ? ? DLp (IR) where H ? is the classical Hilbert-transform of ? . It is proved that H is an isomorphism from (DLp (IR))' onto itself. The Riesz-Titchmarch classical inversion formula for the Hilbert-transform interpreting the limits in the distributional sense, is proved to be valid for the class of distributions in (DLp (IR))' (1
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