arXiv 1002.28042010-02math.FA

Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

U. Battisti, S. Coriasco

备注：: 24 pages, picture changed, added references, corrected typos
发表信息：: Ann. Global Anal. Geom. 40, 2, 223-249 (2011)
DOI：: 10.1007/s10455-011-9255-3

英文摘要：

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function. Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator belonging the mentioned class in the case m_1=m_2.

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