Resolvent estimates on symmetric spaces of noncompact type
type: Item
instance of: scholarly article
title: Resolvent estimates on symmetric spaces of noncompact type
zbMATH Open document ID: 1301.47045
author: Koichi Kaizuka
published in: Journal of the Mathematical Society of Japan
publication date: 2014-09-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1406206976
review text: The author establishes a resolvent estimate for the Laplace-Beltrami operator or more general elliptic Fouirer multipliers on symmetric spaces of noncompact type. Then Kato theory implies time-global smoothing estimates for the corresponding dispersive equations, especially the Schrödinger evolution equation. For low-frequency estimates, a pseudo-dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show weighted \(L^2\)-continuity of the modified Radon transform and fractional integral operators.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6350044
zbMATH Keywords: resolvent
zbMATH Keywords: symmetric space
zbMATH Keywords: dispersive equation
zbMATH Keywords: smoothing effect
zbMATH Keywords: limiting absorption principle
reviewed by: Shangquan Bu
MaRDI profile type: Publication
OpenAlex ID: W2069197094
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DOI: 10.2969/JMSJ/06630895
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description: scientific article; zbMATH DE number 6350044