Harmonic analysis associated with the Weinstein type operator on Rd

 We consider the Weinstein type operator ??;d on Rd. We build transmutation operators R? which turn out to be transmutation operator between ??;d and the Laplacian?d. Using this transmutation operators and its dual tR?, we develop a new commutative harmonic analysis on Rd corresponding to the operator ??;d

Harmonic analysis associated with the Weinstein type operator on Rd

 We consider the Weinstein type operator ??;d on Rd. We build transmutation operators R? which turn out to be transmutation operator between ??;d and the Laplacian?d. Using this transmutation operators and its dual tR?, we develop a new commutative harmonic analysis on Rd corresponding to the operator ??;d

Titchmarsh Theorems and K-Functionals for the Two-Sided Quaternion Fourier Transform

The purpose of this paper is to study the Quaternion Fourier transforms of functions that satisfy Lipschitz conditions of certain orders. Thus we study the Quaternion Fourier transforms of Lipschitz function in the functions space Lr(R2; H), where H a quaternion algebra which will be specified in due course. Our investigation into the problem was motivated by a theorem proved by Titchmarsh [[29], Theorem 85] for Lipschitz functions on the real line. we will give also some results on calculation of the K-functional which have number of applications of interpolation theory. In particular some recent problems in image processing and singular integral operators require the computation of suitable K-functionals. In this paper we will give some results concerning the equivalence of a K-functional and the modulus of smoothness constructed by the Steklov function

Analogues of Miyachi and Cowling-Price theorems for the generalized Dunkl transform

In this paper,we consider the generalized Dunkl transform which satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Cowling-Price’s theorem, Miyachi’s theorem are obtained for the generalized Dunkl transform.The techniques of the proofs are based on the properties of the generalized Dunkl kernel, the relation between the generalized Dunkl transform with the classical Dunkl transform. The results of this paper are new, and they have novelty and generalize some results exist in the literature

Hardy’s theorem for the generalized Bessel transform on the half line

In this paper, we give a generalization of a qualitative uncertainty principle namely Hardy’s theorem, which asserts that a function and its Fourier transform cannot both be very small, for the generalized Bessel transform on the half line

Analogues of Miyachi and Cowling-Price theorems for the generalized Dunkl transform

In this paper,we consider the generalized Dunkl transform which satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Cowling-Price’s theorem, Miyachi’s theorem are obtained for the generalized Dunkl transform.The techniques of the proofs are based on the properties of the generalized Dunkl kernel, the relation between the generalized Dunkl transform with the classical Dunkl transform. The results of this paper are new, and they have novelty and generalize some results exist in the literature

AN ANALOGUE OF COWLING-PRICE’S THEOREM FOR THE Q-FOURIER-DUNKL TRANSFORM

The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using theheat kernel associated to the Q-Fourier-Dunkl operator, we have established an analogue of Cowling-Price, Miyachi and Morgan theorems on $\mathbb{R}$ by using the heat kernel associated to the Q-Fourier-Dunkl transform