Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Opuscula Mathematica

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Eigenvalue asymptotics for potential type operators on lipschitz surfaces of codimension greater than 1

Rozenblum G., Tashchiyan G.

Opuscula Mathematica

2018

Vol. 38, no. 5

733--758

For potential type integral operators on a Lipschitz submanifold the asymptotic formula for eigenvalues is proved. The reasoning is based upon the study of the rate of operator convergence as smooth surfaces approximate the Lipschitz one.

Eigenvalue asymptotics for the Sturm-Liouville operator with potential having a strong local negative singularity

Nursultanov M., Rozenblum G.

Opuscula Mathematica

2017

Vol. 37, no. 1

109--139

We find asymptotic formulas for the eigenvalues of the Sturm-Liouville operator on the finite interval, with potential having a strong negative singularity at one endpoint. This is the case of limit circle in H. Weyl sense. We establish that, unlike the case of an infinite interval, the asymptotics for positive eigenvalues does not depend on the potential and it is the same as in the regular case. The asymptotics of the negative eigenvalues may depend on the potential quite strongly, however there are always asymptotically fewer negative eigenvalues than positive ones. By unknown reasons this type of problems had not been studied previously.