Spectral theory of multiplication operators on Hardy-Sobolev spaces

2017/09/07 by Guangfu Cao, Li He, Cao, Guangfu +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.FA

paper · pdf · doi:10.48550/arxiv.1709.02047

24 pages

arxiv created 2017/09/07 · openalex publication_date 2017/09/07 · arxiv updated 2017/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a pointwise multiplier φ of the Hardy-Sobolev space H²_β on the open unit ball \bn in \cn, we study spectral properties of the multiplication operator M_φ: H²_β→ H²_β. In particular, we compute the spectrum and essential spectrum of M_φ and develop the Fredholm theory for these operators.

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• Fredholm multiplication operators on Banach spaces of analytic functions on the open unit disk

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