Spectral Properties of Hypoelliptic Operators |
| |
Authors: | J-P Eckmann M Hairer |
| |
Institution: | (1) Département de Physique Théorique, Université de Genève, Geneve, Switzerland. E-mail: Jean-Pierre.Eckmann@physics.unige.ch; Martin.Hairer@physics.unige.ch, CH;(2) Section de Mathématiques, Université de Genève, Geneve, Switzerland, CH |
| |
Abstract: | We study hypoelliptic operators with polynomially bounded coefficients that are of the form K=∑
i=1
m
X
i
T
X
i
+X
0+f, where the X
j
denote first order differential operators, f is a function with at most polynomial growth, and X
i
T
denotes the formal adjoint of X
i
in L
2. For any ɛ>0 we show that an inequality of the form ||u||δ,δ≤C(||u||0,ɛ+||(K+iy)u||0,0) holds for suitable δ and C which are independent of yR, in weighted Sobolev spaces (the first index is the derivative, and the second the growth). We apply this result to the Fokker-Planck
operator for an anharmonic chain of oscillators coupled to two heat baths. Using a method of Hérau and Nier HN02], we conclude
that its spectrum lies in a cusp {x+iy|x≥|y|τ−c,τ(0,1],cR}.
Received: 30 July 2002 / Accepted: 18 October 2002 Published online: 25 February 2003
RID="*"
ID="*" Present address: Mathematics Research Centre of the University of Warwick
Communicated by A. Kupiainen |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|