Related papers: Evans Functions, Jost Functions, and Fredholm Dete…
This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…
In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…
A general formulation of the linear model with functional (random) explanatory variable $X = X(t), t \in T$ , and scalar response Y is proposed. It includes the standard functional linear model, based on the inner product in the space…
An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,…
Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…
A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral…
A distributional equation as a criterion for invariant measures of Markov processes associated to L\'evy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
For a two-dimensional quantum mechanical problem, we obtain a generalized power-series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similarly to the standard effective range…
In the framework of the resolvent approach it is introduced a so called twisting operator that is able, at the same time, to superimpose \`a la Darboux $N$ solitons to a generic smooth decaying potential of the Nonstationary Schr\"odinger…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
We perform error analyses explaining some previously mysterious phenomena arising in numerical computation of the Evans function, in particular (i) the advantage of centered coordinates for exterior product and related methods, and (ii) the…
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…
We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some aspects of twistor theory as well as some extensions of Bessel…
This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…
Using the Fitzpatrick function, we characterize the solutions for different classes of deterministic and stochastic differential equations driven by maximal monotone operators (or in particular subdifferential operators) as the minimum…
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 give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
We generalise well-known integrals of Ingham-Siegel and Fisher-Hartwig type over the unitary group $U(N)$ with respect to Haar measure, for finite $N$ and including fixed external matrices. When depending only on the eigenvalues of the…
In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm is known and is based on an EM algorithm when involved functions are non-negative and integrable. With this algorithm we…