Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane - Archive ouverte HAL Access content directly
Journal Articles European Journal of Mathematics Year : 2015

Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane

Abstract

The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as Lm[u] = ∆u + (m/x) ∂xu = 0, where m ∈ C. We generalize results known for m ∈ R to m ∈ C. We give explicit expressions of fundamental solutions for Weinstein operators and their estimates near singularities, then we prove a Green's formula for GASP in the right half-plane H + for Re m < 1. We establish a new decomposition theorem for the GASP in any annular domains for m ∈ C, which is in fact a generalization of the Bôcher 's decomposition theorem. In particular , using bipolar coordinates, we prove for annuli that a family of solutions for GASP equation in terms of associated Legendre functions of first and second kind is complete. For m ∈ C, we show that this family is even a Riesz basis in some non-concentric circular annuli.
Fichier principal
Vignette du fichier
CR5.pdf (497.91 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00940237 , version 1 (03-02-2014)
hal-00940237 , version 2 (08-03-2016)

Identifiers

Cite

Slah Chaabi, Stephane Rigat. Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane. European Journal of Mathematics, 2015, 1 (3), pp.582-640. ⟨10.1007/s40879-015-0053-5⟩. ⟨hal-00940237v2⟩
449 View
162 Download

Altmetric

Share

Gmail Facebook X LinkedIn More