Related papers: Overdetermined fractional Serrin problem
We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…
Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…
We show that a class of de Branges spaces, generated by means of generalized Fourier transforms associated with perturbed Bessel differential equations, has the properties of oversampling and aliasing.
We revisit the properties of Bessel-Riesz operators and refine the proof of the boundedness of these operators on generalized Morrey spaces using Young's inequality. We also obtain an estimate for the norm of these operators on generalized…
The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…
In this article, the operator $\Diamond_{B}^{k}$ is introduced and named as the Bessel diamond operator iterated $k$ times and is defined by $ \Diamond_{B}^{k} = [ (B_{x_{1}} + B_{x_{2}} + ... + B_{x_{p}})^{2} - (B_{x_{p + 1}} + ... +…
In the present article, we assume that the first approximation of the scattering operator is given and that it has the logarithmic divergence. This first approximation allows us to construct the so called deviation factor. Using the…
The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…
We derive a Bernstein von-Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrized by a finite-dimensional parameter of interest. We apply our results to hierarchical models containing non-linear operators,…
Using Jacobi's identity we derive a simple expression for the Bessel functions of integer order in terms of combinations of powers and hyperbolic functions of the same argument.
We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
This paper establishes a rigorous functional analytic framework for weighted Weyl-Sonine fractional operators on semi-infinite intervals. While the classical Phillips functional calculus relies strictly on completely monotonic Bernstein…
In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…
This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg…
We consider a complex of pseudo-differential operators associated with an overdetermined system of operators defined on the torus. We characterize the global solvability of this complex when the system has constant coefficients.…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…