Gaussian estimates and regularized groups

Authors:
Quan Zheng and Jizhou Zhang

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1089-1096

MSC (1991):
Primary 47D03, 47F05

DOI:
https://doi.org/10.1090/S0002-9939-99-04649-3

MathSciNet review:
1473683

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if a bounded analytic semigroup on satisfies a Gaussian estimate of order and is the generator of its consistent semigroup on , then generates a -regularized group on where . We obtain the estimate of () and the -independence of , and give applications to Schrödinger operators and elliptic operators of higher order.

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Additional Information

**Quan Zheng**

Affiliation:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China

Email:
qzheng@hust.edu.cn

**Jizhou Zhang**

Affiliation:
Department of Mathematics, Hubei University, Wuhan 430062, People’s Republic of China

Email:
zhangjz@hubu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-99-04649-3

Keywords:
Gaussian estimate,
regularized group,
analytic semigroup,
differential operator

Received by editor(s):
February 27, 1997

Received by editor(s) in revised form:
July 14, 1997, and July 22, 1997

Additional Notes:
This project was supported by the National Science Foundation of China

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1999
American Mathematical Society