Journal of the Mathematical Society of Japan

Resolvent estimates on symmetric spaces of noncompact type

Koichi KAIZUKA

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Abstract

In this article we prove resolvent estimates for the Laplace-Beltrami operator or more general elliptic Fourier multipliers on symmetric spaces of noncompact type. Then the Kato theory implies time-global smoothing estimates for 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 a weighted $L^{2}$-continuity of the modified Radon transform and fractional integral operators.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 3 (2014), 895-926.

Dates
First available in Project Euclid: 24 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1406206976

Digital Object Identifier
doi:10.2969/jmsj/06630895

Mathematical Reviews number (MathSciNet)
MR3238321

Zentralblatt MATH identifier
1301.47045

Subjects
Primary: 47A10: Spectrum, resolvent
Secondary: 43A85: Analysis on homogeneous spaces 35B65: Smoothness and regularity of solutions

Keywords
resolvent symmetric space dispersive equation smoothing effect limiting absorption principle

Citation

KAIZUKA, Koichi. Resolvent estimates on symmetric spaces of noncompact type. J. Math. Soc. Japan 66 (2014), no. 3, 895--926. doi:10.2969/jmsj/06630895. https://projecteuclid.org/euclid.jmsj/1406206976


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