In this paper we establish a mean value property for the functions which is satisfied to Laplace–Bessel equation. Our results involve generalized divergence theorem and second Green’s identities relating bulk with boundary of region on differential Bessel operators act. Also design fractional weighted operator, study its boundedness, obtain maximal inequality spherical get boundedness. The conn...

Purpose Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based complete orthonormal system of Dunkl kernels generalizing classical exponential defining Fourier series. Design/methodology/approach Although difficulties related to settings, techniques used by K. Sato were still efficient in this case establish inequalities which have expected simila...

In this paper we introduce a generalized Laplace transform in order to work with very general fractional derivative, and obtain the properties of new transform. We also include corresponding convolution inverse formula. particular, definition for improves previous results. Additionally, deal harmonic oscillator equation, showing that its allow one solve differential equations.

We demonstrate a method for generation of beams of light with large angular momenta. The method utilizes whispering gallery mode resonators that transform a plane electromagnetic wave into high order Bessel beams. Interference pattern among the beams as well as shadow pictures induced by the beams are observed and studied.