Cwikel-Solomyak estimates on tori and Euclidean spaces

2020/08/11 by Fedor Sukochev, Dmitriy Zanin, Sukochev, Fedor +1 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.04494

openalex publication_date 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revise Cwikel-type estimate for the singular values of the operator (1-Δ_\mathbbT^d)^-(d)/(4)M_f(1-Δ_\mathbbT^d)^-(d)/(4) on the torus \mathbbT^d for the ideal L_1,∞, established by M.Z. Solomyak in even dimensions in \citeSolomyak1995, and extend it to odd dimensions. We obtain a new result for (symmetrized) Cwikel type estimates for Laplacians on ℝ^d for arbitrary positive integer d.

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• Connes Integration Formula without singular traces
• Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger\n Operators on Curved Noncommutative Tori

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