and operator norm estimates

for the complex time heat operator

on homogeneous trees

Author:
Alberto G. Setti

Journal:
Trans. Amer. Math. Soc. **350** (1998), 743-768

MSC (1991):
Primary 43A85, 35K05; Secondary 39A12

MathSciNet review:
1443889

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a homogeneous tree of degree greater than or equal to three. In this paper we study the complex time heat operator induced by the natural Laplace operator on . We prove comparable upper and lower bounds for the norms of its convolution kernel and derive precise estimates for the operator norms of for belonging to the half plane In particular, when is purely imaginary, our results yield a description of the mapping properties of the Schrödinger semigroup on .

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Additional Information

**Alberto G. Setti**

Affiliation:
Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italia

Email:
setti@dsdipa.mat.unimi.it

DOI:
http://dx.doi.org/10.1090/S0002-9947-98-02042-X

Keywords:
Homogeneous trees,
complex time heat operator,
spherical Fourier analysis

Received by editor(s):
June 10, 1996

Additional Notes:
Work partially supported by the Italian M.U.R.S.T

Article copyright:
© Copyright 1998
American Mathematical Society