Transmutation operators as a solvability concept of abstract singular equations

One of the methods of studying differential equations is the transmutation operators method. Detailed study of the theory of transmutation operators with applications may be found in the literature. Application of transmutation operators establishes many important results for different classes of differential equations including singular equations with Bessel operato

An Analog of Titchmarsh's Theorem for the Jacobi-Dunkl Transform in the Space L2α,β(R)

In this paper, using a generalized Jacobi-Dunkl translation operator, we prove an analog of Titchmarsh's theorem  for functions satisfying the Jacobi-Dunkl Lipschitz  condition in $L^{2}(\R,A_{\alpha ,\beta}(t)dt), \alpha \geq \beta\geq-\frac{1}{2}, \alpha \neq -\frac{1}{2}.$</span

Characterization of (δ,γ)-Dini-Lipschitz Functions in Terms of Their Jacobi-Dunkl Transforms

In this paper, we are going to define a generalized Dini-Lipschitz class and give a characterization for functions belonging to by means of an asymptotic estimating growth of the norm of their Jacobi-Dunkl transforms

Integral geometry on discrete Grassmannians in Z^n

We study the Radon transform R on the discrete Grassmannian of rank-d affine sublattices of Z^n for 0 < d < n. Various natural questions are treated, such as the definition and properties of R and its dual transform R^*, function space setting, support theorems and inversion formulas

A Real Paley-Wiener Theorem for the Generalized Dunkl Transform

In this article, we prove a real Paley-Wiener theorem for the generalized Dunkl transform on R

Beurling’S Theorem and Lp− Lqmorgan’S Theorem for the Generalized Bessel-Struve Transform

The generalized Bessel-Struve transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling’s theorem and Lp− LqMorgan’s theorem obtained for the generalized Bessel-Struve transform