Related papers: Overdetermined fractional Serrin problem

We construct an operational calculus supported on the algebraic operational calculus introduced by Bengochea and Verde. With this operational calculus we study the solution of certain Bessel type equations.

The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…

This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

Mellin convolution equations acting in Bessel potential spaces are considered. The study is based upon two results. The first one concerns the interaction of Mellin convolutions and Bessel potential operators (BPOs). In contrast to the…

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

This paper studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the…

Fix $\lambda>0$. Consider the Bessel operator $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ on $\mathbb{R_+}$, where $\mathbb{R_+}:=(0,\infty)$ and $dm_\lambda:=x^{2\lambda}dx$ with $dx$ the Lebesgue measure. We…

The higher Sylvester waves are discussed. Techniques used involve finite difference operators. For example, using Herschel's theorem, elegant expressions for Euler's rational functions and the Todd operator are found. Derivative expansions…

Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…

We establish that the potential appearing in a fractional Schr\"odinger operator is uniquely determined by an internal spectral data.

We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex $n$-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj\"ostrand.…

The paper is devoted to Mellin convolution operators with meromorphic kernels in Bessel potential spaces. We encounter such operators while investigating boundary value problems for elliptic equations in planar 2D domains with angular…

In this note, we shall prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Hardy and Weber. The formula has strong representation…

Special cases of Weber-Schafheitlin type integrals are evaluated analytically.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator…

In this paper we consider the generalized little Hankel and Berezin type operators on Besov spaces of holomorphic functions on polydiscs and give results about the boundedness of these operators.

We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract…

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to…

The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their applications. Such degrees are…