Imaginary powers of a Laguerre differential operator
type: Item
instance of: scholarly article
title: Imaginary powers of a Laguerre differential operator
zbMATH Open document ID: 1224.42082
author: Błaẓej Wróbel
published in: Acta Mathematica Hungarica
publication date: 2011-02-08T00:00:00Z
review text: Let \(\mathcal{L}_\alpha\) be a self-adjoint extension of the Laguerre differential operator \[ L_\alpha=-\Delta+| x| ^2+\sum_{i=1}^{d} \frac{1}{x_i^2}\Big(\alpha_i^2-\frac{1}{4} \Big), \qquad \alpha_i\in \{-\frac{1}{2}\}\cup [\frac{1}{2},\infty). \] It is proved that \(\mathcal{L}_\alpha^{-i\gamma}\) \((\gamma\in \mathbb{R})\) is a Calderon-Zygmund operator, which implies some results by the general theory.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 5848544
zbMATH Keywords: Laguerre function expansion
zbMATH Keywords: Calderón-Zygmund operator
zbMATH Keywords: imaginary power of a Laguerre differential operator
reviewed by: Ferenc Weisz
MaRDI profile type: Publication
full work available at URL: s10474-009-8203-1
OpenAlex ID: W2088944554
cites work: Q4526789
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cites work: Poisson integrals and Riesz transforms for Hermite function expansions with weights.
cites work: Higher Riesz transforms and imaginary powers associated to the harmonic oscillator
DOI: 10.1007/S10474-009-8203-1
description: scientific article; zbMATH DE number 5848544