Work

Trace bounds for limiting operators on rough domains

Year: 2026

Type: preprint

Abstract: This work concerns a quantitative form of Landau's eigenvalue theorem for spatio-spectral limiting operators. We isolate a simple mechanism that converts the problem of estimating the distribution of eigenvalues of a limiting operator into the problem of bounding the trace of the difference between the operator and its square. This mechanism allows us to analyze limiting operators for domains with fractal boundaries. When the boundaries have finite perimeter, we recover the expected optimal dependence on the scaling parameter.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.02996

Authors: Hughes, Kevin, Israel, Arie, Mayeli, Azita

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, City University of New York

Awards: Collaborative Research: Spectral analysis of limiting operators in higher dimensions, Collaborative Research: Spectral analysis of limiting operators in higher dimensions

OpenAlex ID: W7167594430

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