The Lifshits--Krein trace formula and operator Lipschitz functions

2016/01/04 by V. V. Peller, Peller, Vladmir
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1601.00490

openalex publication_date 2016/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the maximal class of functions f on the real line, for which the Lifshitz--Krein trace formula trace(f(A)-f(B))=∫_{\Bbb R} f'(s)\boldsymbolξ(s) ds holds for arbitrary self-adjoint operators A and B with A-B in the trace class \boldsymbolS₁. We prove that this class of functions coincide with the class of operator Lipschitz functions.

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