Eigenfunctions Of Integral Operator Research Articles

Logarithmic functions are eigenfunctions of integral operators with M-Wright kernels

In this paper, using the Buschman’s theorem for the Laplace transform, we show that the logarithmic functions ϕn(s)=1s∑i=0n(−1)iniΓ(n−i)(1)lni(s),n∈N,are the eigenfunctions of integral operators with M-Wright kernels. Some identities are also given for connections of the Mittag-Leffler functions and ϕn(s).

О сходимости разложений по собственным функциям интегральных операторов с разрывным ядром

О сходимости разложений по собственным функциям интегральных операторов с разрывным ядром

On the ratio of different norms of caloric functions and related eigenfunctions of an integral operator

We investigate the ratio of L1 and L2 norms of the Cauchy problem solutions of heat equations with compact support initial data. The related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral operators is obtained.

On riesz bases of eigenfunctions of integral operators with kernels discontinuous on diagonals

On riesz bases of eigenfunctions of integral operators with kernels discontinuous on diagonals

О базисах Рисса из собственных функций интегральных операторов с ядрами, разрывными на ломаных линиях

О базисах Рисса из собственных функций интегральных операторов с ядрами, разрывными на ломаных линиях

Теорема равносходимости разложений по собственным функциям интегральных операторов с инволюцией, допускающей разрывы

Теорема равносходимости разложений по собственным функциям интегральных операторов с инволюцией, допускающей разрывы

Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals

Simple conditions are found ensuring the equiconvergence of the Fourier expansion of a function in in the eigenfunctions and the associated functions of an integral operator and the expansions of and in the standard trigonometric system.

An initial-value method for integral operators V. Kernels depending upon a parameter

A new technique is presented for the calculation of the eigenvalues and eigenfunctions of integral operators where the kernel is an entire function of the eigenvalue parameter. The method combines a number of results from functions of a complex variable and integral equations with a new technique for converting Fredholm integral equations into an initial-value system of ordinary differential equations. Several pertinent examples are presented which illustrate the efficacy of the procedure.