Cyclicity in the harmonic Dirichlet space

2016/01/25 by Evgueni Abakumov, Omar El-Fallah, Abakumov, Evgueni +5 · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1601.06572

openalex publication_date 2016/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The harmonic Dirichlet space \calD (\mathbbT) is the Hilbert space of functions f ∈ L²(\mathbbT) such that ‖f‖_\calD (\mathbbT)² := ∑_n∈ℤ (1+|n|)|f(n)|² lt; ∞. We give sufficient conditions for f to be cyclic in \calD (\mathbbT), in other words, for \ζⁿf(ζ): n≥ 0\ to span a dense subspace of \calD (\mathbbT).

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