In this paper, we treat a convolution-type operator called the generalized Bessel potential. Our main result is derivation of two different forms its inversion. The first inversion provided in terms an approximative inverse using method improving multiplier. second one employs regularization technique for divergent integrals form appropriate segments Taylor–Delsarte series.

Firstly, we studied the solution of the equation ⊗♦Bu x f x where u x is an unknown unknown function for x x1, x2, . . . , xn ∈ R, f x is the generalized function, k is a positive integer. Finally, we have studied the solution of the nonlinear equation ⊗♦Bu x f x, LΔB kBu x . It was found that the existence of the solution u x of such an equation depends on the condition of f and LΔB kBu x . Mo...

Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pear...

We consider the Schr\"odinger operator on halfline with potential $(m^2-\frac14)\frac1{x^2}$, often called Bessel operator. assume that $m$ is complex. study domains of various closed homogeneous realizations In particular, we prove domain its minimal realization for $|\Re(m)|<1$ and unique $\Re(m)>1$ coincide second order Sobolev space. On other hand, if $\Re(m)=1$ space a subspace infinite co...

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

Abstract. We work out the expression of the generalized Bessel function of B2-type derived in [4]. This is done using Dijskma and Koornwinder’s product formula for Jacobi polynomials and the obtained expression is given by multiple integrals involving only a normalized modified Bessel function and two symmetric Beta distributions. We think of that expression as the major step toward the explici...