Spectral Asymptotics for Quantized Derivatives on Quantum Euclidean Spaces

2025/05/17 by Yongqiang Tian, Tian, Yongqiang · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.11789

openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain spectral asymptotics for the quantized derivatives of elements from the first-order homogeneous Sobolev space on the quantum Euclidean space, extending an earlier result of McDonald, Sukochev and Xiong (Commun. Math. Phys. 2020). Our approach is based on a noncommutative Wiener-Ikehara Tauberian theorem and a recently developed C^∗-algebraic version of pseudo-differential operator theory.

Citations

• A C^*-Algebraic Approach To Principal Symbol Calculus On Filtered Manifolds
• Asymptotics of singular values for quantum derivatives
• Connes' integration and Weyl's laws
• A C^*-algebraic approach to the principal symbol II
• The Connes character formula for locally compact spectral triples
• Singular integrals in quantum Euclidean spaces
• Quasiconformal mappings, operators on hilbert space, and local formulae for characteristic classes
• Nearly weakly orthonormal sequences, singular value estimates, and Calderon-Zygmund operators

Cited by

• Singular value asymptotics on compact smooth Riemaniann manifolds

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