Spectral Estimates and Asymptotics for Integral Operators on Singular Sets
Journal article, 2022

For singular numbers of integral operators of the formu(x)↦∫F1(X)K(XYX−Y)F2(Y)u(Y)u(dY) with a measure μ singular with respect to the Lebesgue measure in ℝN we obtain ordersharp estimates for the counting function. The kernel K(X, Y, Z) is assumed to be smooth in X, Y, Z ≠ 0 and to admit an asymptotic expansion in homogeneous functions in the Z variable as Z → 0. The order in the estimates is determined by the leading homogeneity order in the kernel and geometric properties of the measure μ and involves integral norms of the weight functions F1 and F2. In the selfadjoint case, we obtain asymptotics of the eigenvalues of this integral operator provided that μ is the surface measure on a Lipschitz surface of some positive codimension.


Grigori Rozenblioum

Euler International Mathematical Institute

Chalmers, Mathematical Sciences

Grigory Tashchiyan

Sankt-Peterburgskij Gosudarstvennyj Universitet Telekommunikacij imeni professora Bonch-Bruevicha

Journal of Mathematical Sciences

1072-3374 (ISSN)

Vol. In Press

Subject Categories


Probability Theory and Statistics

Mathematical Analysis



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