Related papers: Integral operators defined "up to a polynomial''
We reprove the essential self-adjointness of the Dirichlet operators of Dirchlet forms for infinite particle systems with superstable and sub-exponentially decreasing interactions.
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
Kernel functions for Laplacian integral operators are constructed on $p$-adic analytic manifolds using charts and transition maps from an atlas with connected nerve complex. In the compact case, an operator of Vladimirov-Taibleson type…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
This paper presents a new formulation of the fractional Laplacian operator $(-\Delta)^s$ in $n$-dimensional space ($n \ge 1$). The proposed formulation expresses $(-\Delta)^s$ as a composition of the classical Laplace differential operator…
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of…
Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the…
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…
We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with…
We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence…