Journal of the Mathematical Society of Japan

Resolvent estimates on symmetric spaces of noncompact type


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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

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

First available in Project Euclid: 24 July 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

resolvent symmetric space dispersive equation smoothing effect limiting absorption principle


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.

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