Related papers: Integral operators defined "up to a polynomial''
We consider quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials. When a slowly decaying potential function is given, we prove the nonexistence of the wave operators, under the…
Many attempts to introduce fundamental nonlocality into quantum (or classical) field theory are based on the assumption that exponentials of the d'Alembertian are positive-definite, so that these operators can be employed without…
In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional $g$-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
In the present work we characterized full operators and we showed some properties that have nonfull injectives operators. With the results developed for full operators, we affirmatively respond two questions formulated by Bravo and Feintuch…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
We consider the elliptic differential operator defined as the sum of the minimum and the maximum eigenvalue of the Hessian matrix, which can be viewed as a degenerate elliptic Isaacs operator, in dimension larger than two. Despite of…
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…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
We prove an entanglement principle for fractional Laplace operators on $\mathbb R^n$ for $n\geq 2$ as follows; if different fractional powers of the Laplace operator acting on several distinct functions on $\mathbb R^n$, which vanish on…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the…
Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of monotone operators acting on different spaces and linear…
In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on a complete Finsler manifold. Depending on the positive $\lambda$ parameter of the inclusion, we establish non-existence, as well as…
We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…