Related papers: On the Weber integral equation and solution to the…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can…
We study Mittag-Leffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting…
In a recent paper we unified Bessel functions of different orders .Here we extend the unification to other linairely independant solutions to Bessel equation, Neumann's and Hankel's functions
The Weber problem consists of finding a point in $\mathbbm{R}^n$ that minimizes the weighted sum of distances from $m$ points in $\mathbbm{R}^n$ that are not collinear. An application that motivated this problem is the optimal location of…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal…
In this paper we obtain sharp results for Waring's problem over general finite rings, by using a combination of Artin-Wedderburn theory and Hensel's lemma and building on new proofs of analogous results over finite fields that are achieved…
The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex…
We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce the matrix integral to the…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance…
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…
In this paper we examine an inverse problem in the modular theory of von Neumann algebras in the case of finite factors. First we give a characterization of cyclic and separating vectors for finite factors in terms of operators associated…
Several important problems in partial differential equations can be formulated as integral equations. Often the integral operator defines the solution of an elliptic problem with specified jump conditions at an interface. In principle the…
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…
In this work, we characterize the existence of solution for a certain variational inequality by means of a classical minimax theorem. In addition, we propose a numerical algorithm for the solution of an inverse problem associated with a…
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.