Eigenvalues of the Birman-Schwinger operator for singular measures: The noncritical case
Journal article, 2022

For operators of the form T=TA,P=A⁎PA with pseudodifferential operator A of negative order −l in a domain in RN, 2l≠N, and a singular measure P, an estimate of eigenvalues is found with an order depending on the dimensional characteristics of the measure P and the coefficient depending on an integral norm of the density of P with respect to the Hausdorff measure of an appropriate dimension. These estimates are used to establish asymptotic formulas for the eigenvalues of T for the case when P is supported on a Lipschitz surface of some codimension and on certain sets of a more complicated structure. In one of applications, a version of the CLR estimate for singular measures is proved.

Eigenvalues asymptotics

Singular measure

Pseudodifferential operator

Eigenvalues estimates


Grigori Rozenblioum

Chalmers, Mathematical Sciences

Sirius University of Science and Technology

Saint Petersburg State University - Spsu

Grigory Tashchiyan

Sankt-Peterburgskij Gosudarstvennyj Universitet Telekommunikacij imeni professora Bonch-Bruevicha

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 283 12 109704

Subject Categories


Probability Theory and Statistics

Mathematical Analysis



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