It is well known that the generalized translation operator T associated with the Bessel function of the first kind is positive in the sense if f > 0, then Tf > 0. This property is easily seen when we write Tf as an integral representation with a kernel involving the area of some triangle ([1],[9]) and has several applications in many mathematical fields such that hypergroup structure, heat equa...

We demonstrate the transfer of orbital angular momentum from a light beam to a trapped low-index particle. The particle is trapped in a dark annular region of a high-order Bessel beam and rotates around the beam axis due to scattering from the helical wave fronts of the light beam. A general theoretical geometrical optics model is developed that, applied to our specific situation, corroborates ...

The non-local problem is considered for the partial differential equation of mixed-type with Bessel operator and fractional order. An explicit solution represented by Fourier-Bessel series in given domain. It established connection between data unique solvability problem.

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...

Given α > −1, consider the second order differential operator in (0,∞) Lαf ≡ ( x 2 d 2 dx2 + (2α+ 3)x d dx + x + (α+ 1) ) (f), which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking Lα as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These bounde...

For a delta operator aD − bD we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D − 1 2D 2 we show that the corresponding Bessel–Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions νt, t > 0, for which {yn(t)}, the Bessel polynomials at t, is the moment ...

The boundedness of Bessel–Riesz operators defined on Lebesgue spaces and Morrey in measure metric is discussed this research study. maximal operator traditional dyadic decomposition are used to study the Bessel-Riesz operators. We investigate interaction between kernel space parameters get results see how affects kernel-bound

We consider a plane wave diffraction problem by a union of several infinite strips. The problem is formulated as a boundary-transmission one for the Helmholtz equation in a Bessel potential space setting and where Neumann conditions are assumed on the strips. Using arguments of strong ellipticity and different kinds of operator relations between convolution type operators, it is shown the well-...