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The radon split of radially acting linear integral operators on H2 with uniformly bounded double norms

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The radon split of radially acting linear integral operators on H2 with uniformly bounded double norms

Ghassel, Ali (1999) The radon split of radially acting linear integral operators on H2 with uniformly bounded double norms. Masters thesis, Concordia University.

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Abstract

This M.Sc. thesis treats the feasibility of the Radon Split for solving radial integral equation involving radially acting integral operator on the Hardy-Lebesgue Class [Special characters omitted.] of the half-upper plane [Special characters omitted.] . In this process, we take a scrutinizing look at [Special characters omitted.] by means of the conformal map [Special characters omitted.] taking [Special characters omitted.] . We demonstrate that [Special characters omitted.] -functions f always possess a.e. unique boundary values [Special characters omitted.] [Special characters omitted.] as [Special characters omitted.] from within [Special characters omitted.] . These boundary values are also angular limit functions in the [Special characters omitted.] -sense--i.e. [Special characters omitted.] as [Special characters omitted.] from within [Special characters omitted.] . Concomitantly, the [Special characters omitted.] -parameter family of [Special characters omitted.] -kernels [Special characters omitted.] with uniformly bounded double norms, have unique angular limit [Special characters omitted.] -kernels [Special characters omitted.] in the [Special characters omitted.] -sense--i.e. [Special characters omitted.] = [Special characters omitted.] [arrow right] 0 as [Special characters omitted.] from within [Special characters omitted.] . These properties are consequences of the inverse Mellin-Transform, which transformation originates in Fourier-Plancherel Theorem for [Special characters omitted.] and [Special characters omitted.] . Because of this Mellin-Transform representation of [Special characters omitted.] and [Special characters omitted.] we may regard [Special characters omitted.] as the three entities: [Special characters omitted.] and [Special characters omitted.] , where the first two are Hilbert spaces and the third is a dual system with [Special characters omitted.] Consequently, we look upon [Special characters omitted.] as the Banach algebra [Special characters omitted.] and further as the Hilbert space [Special characters omitted.] . We successfully construct for every radial linear integral operator K of finite rank on [Special characters omitted.] , its transpose K T in [Special characters omitted.] as well as its adjoint K * in [Special characters omitted.] , which leans heavily on the interaction of * and T in [Special characters omitted.] . We prove a necessary and sufficient condition as to when an element of [Special characters omitted.] is radially representable. And finally, we construct Fredholm Resolvents not only finite-dimensional [Special characters omitted.] but also, by means of the Radon Split, the Fredholm Resolvents of any [Special characters omitted.] and that of its transpose K T in terms of [Special characters omitted.] . Herein, the Fredholm Alternatives are induced by the derivations.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Ghassel, Ali
Pagination:vii, 132 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Mathematics and Statistics
Date:1999
Thesis Supervisor(s):Keviczky, Attila
ID Code:1035
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:16
Last Modified:08 Dec 2010 10:18
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