On space of parabolic potentials generated by the generalized translation operator

ABSTRACT ON SPACE OF PARABOLIC POTENTIALS GENERATED BY THE GENERALIZED TRANSLATION OPERATOR Sinem SEZER Ph. D. Thesis in Mathematics Adviser: Assoc. Prof. Dr. İlham ALIYEV May 2005, 53 Pages The work presented in this thesis is on the space of parabolic potentials. The aim of this thesis is to characterize the space of parabolic potentials generated by the generalized translation operator. Therefore, firstly, definitions of B-parabolic potentials and the space of B-parabolic potentials are given. Then anisotropic and weighted finite difference together with the suitable family of operators are cons tituted. Finally, the main result of this thesis is obtained by using concepts above mentioned. KEY WORDS: Laplace-Bessel differential operator, Generalized translation operator, Fourier-Bessel transform, B-parabolic potential, weighted Lp-space, ani sotropic and weighted finite difference. COMMITTEE : Prof. Dr. İlham ALIYEV (Adviser) Prof. Dr. Velİ KURT Prof. Dr. A. Aziz ERGİN Prof. Dr. Orhan GÖLBAŞI Doç. Dr. Abdulkadir Ceylan ÇÖKEN ii