Gaussian estimates and regularized groups
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- by Quan Zheng and Jizhou Zhang PDF
- Proc. Amer. Math. Soc. 127 (1999), 1089-1096 Request permission
Abstract:
We show that if a bounded analytic semigroup $\{T(z)\}_{ \operatorname {Re}z>0}$ on $L^2({\boldsymbol {\Omega }} )$ $({\boldsymbol {\Omega }} \subset \mathbf {R} ^n)$ satisfies a Gaussian estimate of order $m$ and $A_p$ is the generator of its consistent semigroup on $L^p({\boldsymbol {\Omega }} )$ $(1\le p<\infty )$, then $iA_p$ generates a $(1-A_p)^{-\alpha }$-regularized group on $L^p({\boldsymbol {\Omega }} )$ where $\alpha >2n |\frac {1}{2}-\frac {1}{p}|$. We obtain the estimate of $(\lambda -A_p)^{-1}$ ($|\operatorname {arg}\lambda |<\pi$) and the $p$-independence of $\sigma (A_p)$, and give applications to Schrödinger operators and elliptic operators of higher order.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- 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