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International Conference: 2004 - Dynamical Systems and Applications
July 5-10, 2004

Antalya, Turkey

Organizers
Akca Haydar, Basem S. Attili, Boucherif Abdelkader, Cho Yeol Je, Covachev Valery, Gyori Istvan, Maksimov Vyacheslav, Stavroulakis Ioannis P.

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Wavelet-type transform generated by the Poisson kernel
by
Melih Eryigit
Akdeniz University Dept. of Mathematics Antalya/TURKEY
Coauthors: Ilham A. Aliev

Let \mu be a signed Borel measure on R1 such that supp \mu subset [0, \infty), |\mu|(R1) < \infty and \mu( R1 ) \equiv \intR1d\mu(t)=0. Let further, P (y, t) be the classical Poisson Kernel defined by F(P(., t))(y)=exp (-t|y|), (y in Rn , t > 0 and F being the Fourier transform). We define
(W\mu f)(x, \eta)= ó
õ

Rn+1  
 P(y, t)f(x-\etay)dyd\mu(t), (\eta > 0, x in Rn ).

In this work we obtain an explicit inversion formula for the wavelet -type transform W\mu f. L2 and Lp, 1 <= p <= \infty cases are examined separately. In subsequent publications we plan to give some applications of our results to inversion problem of Riesz potentials.

Date received: March 15, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canu-57.