Trace expansions for elliptic cone operators with stationary domains
نویسندگان
چکیده
منابع مشابه
Trace Expansions for Elliptic Cone Operators with Stationary Domains
Abstract. We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand ...
متن کاملResolvents of Elliptic Cone Operators
We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.
متن کاملAdjoints of Elliptic Cone Operators
We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x Diffmb (M ;E), ν > 0, initially defined as an unbounded operator A : C∞ c (M ;E) ⊂ x L b (M ;E) → xL b (M ;E), μ ∈ R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.
متن کاملFull asymptotic expansion of the heat trace for non–self–adjoint elliptic cone operators
The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...
متن کاملResolvent Expansions and Trace Regularizations for Schrödinger Operators
We provide a direct approach to a study of regularized traces for long range Schrödinger operators and small time asymptotics of the heat kernel on the diagonal. The approach does not depend on multiple commutator techniques and improves upon earlier treatments by Agmon and Kannai, Melin, and the authors.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2010-05283-3