The study Bessel potentials with the aid of weigted wavelet transform

ABSTRACT THE STUDY ON BESSEL POTENTIALS WITH THE AID OF WEIGHTED WAVELET TRANSFORM Melih ERYÎ?ÎT Ph.D. Thesis in Mathematics Adviser: Assoc.Prof.Dr. ilham ALIYEV April-2004, 44 pages The classical Bessel potentials are known as an important technical tool in Analy sis and its applications. An familar problem concerning the Bessel potentials is to obtain explicit inversion for them. A number of approaches to this problem are known. In this work we develop a new approach to the aforementioned problem and invert Bessel potentials by means of the so-called weighted wavelet transforms. KEY WORDS: Bessel potentials, fractional integral and derivative, weighted wavelet transform, Calderon-type reproducing formula, Gauss- Weierstrass kernel COMMITTEE : Assoc.Prof.Dr. Ilham ALIYEV Prof. Dr. Veli KURT Prof. Dr. Abdullah A. ERGÎN Prof. Dr. Serpil PEHLİVAN Prof. Dr. Daniyal M. ÎSRAFÎLOV 11