Spectral asymptotics and estimates for matrix Birman-Schwinger operators with singular measures

2025/08/20 by Grigori Rozenblum, Rozenblum, Grigori, Grigory Tashchiyan +1
Computer Science · Mathematics · #47G30 #47G40 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2508.14517

openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We consider operators of the form T=A^*(Vμ)A in ℝ^N, where A is a pseudodifferential operator of order -l, μ is a compactly supported singular measure, order s>0 Ahlfors-regular, and V is a weight function on the support of μ. The scalar type operator A and the weight function V are supposed to be m× m matrix valued. We establish Weyl type asymptotic formulas for singular numbers and eigenvalues of T for μ being the natural measure on a compact Lipschitz surface. For a general Ahlfors-regular measure μ, we prove that the previously found upper spectral estimates are order sharp.

Citations

• Spectrum of the perturbed Landau-Dirac operator
• Spectral properties of the resolvent difference for singularly perturbed operators
• Spectral estimates and asymptotics for integral operators on singular sets
• Spectral estimates and asymptotics for stratified Lie groups
• Eigenvalues of the Birman-Schwinger operator for singular measures: the noncritical case
• Eigenvalues of singular measures and Connes noncommutative integration
• On the spectrum of Bargmann-Toeplitz operators with symbols of a variable sign

Related

• Eigenvalues of the Birman-Schwinger operator for singular measures: the noncritical case
• Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case
• Spectral estimates and asymptotics for integral operators on singular sets
• Singular equivariant asymptotics and Weyl's law
• Spectral asymptotics of pseudodifferential operators with discontinuous symbols