Integral representation and asymptotic behavior of harmonic functions in half space

DOI10.1016/j.jde.2014.05.047zbMath1297.31011OpenAlexW2005748607MaRDI QIDQ399942

Guan Tie Deng, Kit Ian Kou, Yan Hui Zhang

Publication date: 20 August 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2014.05.047

zbMATH Keywords

harmonic functionsintegral representationsCarleman's formulaNevanlinna's representation

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (6)

Asymptotic behavior of fractional Laplacians in the half space ⋮ Integral representations of a class of harmonic functions in the half space ⋮ Explicit solutions of the Dirichlet-Schrödinger problem via the new cylindrical Poisson-Schrödinger kernel method ⋮ Hayman theorem in \(\mathcal{R}_+^{n+1}\) with the Clifford analysis setting ⋮ The generalized Matsaev theorem on growth of subharmonic functions admitting a lower bound in ℝⁿ ⋮ Explicit solutions of cylindrical Schrödinger equation with radial potentials

Cites Work

• A version of Carleman's formula and summation of the Riemann \(\zeta\)-function logarithm on the critical line
• On the lower bound for a class of harmonic functions in the half space
• Integral representation and asymptotic property of analytic functions with order less than two in the half-plane
• Remarks on Carleman’s Formula for Functions in a Half-Plane
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