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Drifted Laplace operators on homogeneous trees
Author(s):
Enrico
Casadio Tarabusi;
Alessandro
Figà-Talamanca
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2165-2175.
MSC (2000):
Primary 43A85;
Secondary 05C05
Posted:
February 8, 2007
MathSciNet review:
2299494
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Abstract:
We determine the spectrum and the resolvent operator of a drifted Laplace operator on a homogeneous tree, obtaining qualitatively different results according to the sign of the drift in the direction of a boundary point.
References:
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- [BCF]
- Paolo Baldi, Enrico Casadio Tarabusi, and Alessandro Figà-Talamanca, Stable laws arising from hitting distributions of processes on homogeneous trees and the hyperbolic half-plane, Pacific J. Math. 197 (2001), no. 2, 257-273. MR 1815256 (2001m:60015)
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- [FN]
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- Alessandro Figà-Talamanca and Massimo Angelo Picardello, Spherical functions and harmonic analysis on free groups, J. Funct. Anal. 47 (1982), no. 3, 281-304. MR 665019 (83m:22018)
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Additional Information:
Enrico
Casadio Tarabusi
Affiliation:
Dipartimento di Matematica ``G. Castelnuovo'', Università di Roma ``La Sapienza'', Piazzale A. Moro 2, 00185 Roma, Italy
Email:
casadio@mat.uniroma1.it
Alessandro
Figà-Talamanca
Affiliation:
Dipartimento di Matematica ``G. Castelnuovo'', Università di Roma ``La Sapienza'', Piazzale A. Moro 2, 00185 Roma, Italy
Email:
sandroft@mat.uniroma1.it
DOI:
10.1090/S0002-9939-07-08811-9
PII:
S 0002-9939(07)08811-9
Keywords:
Homogeneous trees,
Laplace operator,
drifts,
spectrum,
resolvent operator
Received by editor(s):
March 21, 2006
Posted:
February 8, 2007
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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