On translates of the Poisson kernel and zeros of harmonic functions

DOI10.1112/blms/bdl039zbMath1124.42007OpenAlexW2033274472MaRDI QIDQ5297617

Joaquim Bruna, Mark S. Melnikov

Publication date: 12 July 2007

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/blms/bdl039

zbMATH Keywords

Fourier transformCauchy transformdensityHardy spacesharmonic functionsholomorphic functionsPoisson functionsequences of translatesharmonic majorantBeurling--Malliavin density

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items (2)

Phase space distribution of Gabor expansions ⋮ Poisson type generators for \(L^{1}(\mathbb R)\)

Cites Work

• Unnamed Item
• Completeness in \(L^1(\mathbb R)\) of discrete translates
• On translation and affine systems spanning \(L^{1}(\mathbb R)\)
• Vanishing l¹-sums of the Poisson kernel, and sums with positive coefficients
• DECOMPOSITIONS OF FUNCTIONS AS SUMS OF ELEMENTARY FUNCTIONS
• Domination of the supremum of a bounded harmonic function by its supremum over a countable subset

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