Spectral gaps of Schrodinger operators and diffusion operators on abstract Wiener spaces

被引：3

作者：

Gong, Fu-Zhou ^{[1
]}

Liu, Yong ^{[2
]}

Liu, Yuan ^{[1
]}

Luo, De-Jun ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China

[2] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 09期

关键词：

Spectral gap; Schrodinger operator; Abstract Wiener space; Min-max principle; Malliavin calculus;

D O I：

10.1016/j.jfa.2014.02.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we extend the spectral gap comparison theorem of Andrews and Clutterbuck (2011) [2] to the infinite dimensional setting. More precisely, we prove that the spectral gap of Schrodinger operator -L-* + V (L-* is the Ornstein-Uhlenbeck operator) on an abstract Wiener space is greater than that of the one-dimensional operator -d(2)/ds(2) + s d/ds + (V) over tilde (s), provided that (V) over tilde is a modulus of convexity for V. Similar result is established for the diffusion operator -L-* + del F . del. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：5639 / 5675

页数：37

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