Related papers: Representation of multivariate functions via the p…
A representation formula for the solution of the $\infty$-Laplace equation is constructed in a punctured square, the prescribed boundary values being $u=0$ on the sides and $u=1$ at the centre. This so-called $\infty$-potential is obtained…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
An approach for solving a variety of inverse coefficient problems for the Sturm-Liouville equation -y''+q(x)y={\lambda}y with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations…
We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…
We investigate potential spaces associated with Jacobi expansions. We prove structural and Sobolev-type embedding theorems for these spaces. We also establish their characterizations in terms of suitably defined fractional square functions.…
We present the applications of variational-wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell-Poisson equations.
We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are…
Integral equation methods provide an effective framework for solving partial differential equations, but their applicability typically relies on the availability of explicit free-space Green's functions. For coupled systems arising in…
The so$(2,1)$ Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky-Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed…
We probe the application of the calculus of conormal distributions, in particular the Pull-Back and Push-Forward Theorems, to the method of layer potentials to solve the Dirichlet and Neumann problems on half-spaces. We obtain full…
By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate L\'evy processes. Many properties of these polynomials are stated straightforwardly thanks to…
The "potentials" being considered are analogues of classical Riesz potentials of order 1, and the idea is to look at how they might map L^p spaces into Sobolev spaces in various settings.
We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
We present the applications of variational--wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell equations.