Toeplitz Operators Associated with the Hypergeometric Gabor Transform and Applications

In this paper, we introduce and we study the hypergeometric Gabor transform attached to the Cherednik operators in the W-invariant case. We investigate for this transform the main theorems of Harmonic analysis. The theory of the reproducing kernel Hilbert spaces has relatively recent developments in pure and applied mathematics. Motivated by Wong’s approach and involving the theory of RKHS, we introduce, study and giving some applications on the Toeplitz operators associated with the hypergeometric Gabor transform. Results on the \(L^{p}\) $L^p$ -boundedness and \(L^{p}\) $L^p$ -compactness of these Toeplitz operators are also given.