G. Rozenblum

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20242026

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math.SP2026

Negative eigenvalue estimates for polyharmonic SchrÃ¶dinger operators with measure-potentials: the subcritical case

Medet Nursultanov, Grigori Rozenblum

We study spectral estimates for polyharmonic SchrÃ¶dinger operators $- I^^{l} - I^¼$ in the subcritical regime $2 l < N$ . The measure potential $I^¼$ is assumed to satisfy a capacit…

math.SP2025

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

Grigori Rozenblum, Grigory Tashchiyan

We consider operators of the form $T = A^{*} (V I^¼) A$ in $R^{N}$ , where $A$ is a pseudodifferential operator of order $- l$ , $I^¼$ is a…

math.SP2024

Spectral properties of the resolvent difference for singularly perturbed operators

Grigori Rozenblum

We obtain order sharp spectral estimates for the difference of resolvents of singularly perturbed elliptic operators $A + V_{1}$ and $A + V_{2}$ in a do…