GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM

Subject Areas : International Journal of Mathematical Modelling & Computations

S. El ouadih ¹ , R. Daher ² , M. El hamma ³

1 - Department of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II, Casablanca, Morocco;
2 - Department of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II, Casablanca, Morocco
3 - Department of Mathematics, Faculty of Sciences A¨ın Chock,University Hassan II, Casablanca, Morocco.

Received: 2016-07-13 Accepted : 2016-07-13 Published : 2016-07-01

Keywords: generalized translation operator, singular dierential operator, generalized Fourier-Bessel transform, generalized translation operatorsingular dierential operator,

Abstract :

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2on certainclasses of functions.

References:

R. F. Al Subaie and M. A. Mourou, The continuous wavelet transform for a Bessel type

operator on the half line, Mathematics and Statistics 1(4): 196-203, 2013.

V. A. Abilov and F. V. Abilova, Approximation of functions by Fourier-Bessel sums, Izv.

Vyssh. Uchebn. Zaved., Mat., No. 8, 3-9 (2001).

V.S.Vladimirov, Equations of mathematical physics, Marcel Dekker, New York,1971,Nauka,

Moscow,1976.

B.M.Levitan, Expansion in Fourier series and integrals over Bessel functions, Uspekhi

Math.Nauk, 6,No.2,102-143,1951.

Titchmarsh.EC , Introduction to the theory of Fourier integrals . Claredon , oxford, 1948,

Komkniga.Moxow.2005.

R. F. Al Subaie and M. A. Mourou, Transmutation operators associated with a Bessel type

operator on the half line and certain of their applications, Tamsii. oxf. J. Inf. Math. Scien 29

(3) (2013), pp. 329-349.

A.G.Sveshnikov,A.N.Bogolyubov and V.V.Kratsov, Lectures on mathematical physics,

Nauka, Moscow,2004)[in Russian].

Platonov.SS, The Fourier transform of function satisfying the Lipshitz condition on rank 1

symetric spaces , Siberian Math.J.46(2) (2005), 1108-1118.