ar X iv : 0 81 1 . 37 76 v 1 [ m at h . SP ] 2 3 N ov 2 00 8 TRACE EXPANSIONS FOR ELLIPTIC CONE OPERATORS I
نویسنده
چکیده
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 the component of finite rank in the case where the domain is stationary. The results make use, and develop further, our previous investigations on the analytic and geometric structure of the resolvent. The analysis of nonstationary domains, considerably more intricate, is pursued elsewhere.
منابع مشابه
ar X iv : 0 81 1 . 12 76 v 1 [ m at h - ph ] 8 N ov 2 00 8 Correlation Functions for β = 1 Ensembles of Matrices of Odd Size
Using the method of Tracy and Widom we rederive the correlation functions for β = 1 Hermitian and real asymmetric ensembles of N ×N matrices with N odd.
متن کاملar X iv : 0 81 0 . 17 89 v 1 [ m at h . SP ] 1 0 O ct 2 00 8 SPECTRAL THEORY OF ELLIPTIC OPERATORS IN EXTERIOR DOMAINS
We consider various closed (and self-adjoint) extensions of elliptic differential expressions of the type A = P 06|α|,|β|6m(−1) Daα,β(x)D β , aα,β(·) ∈ C ∞(Ω), on smooth (bounded or unbounded) domains Ω in R with compact boundary ∂Ω. Using the concept of boundary triples and operator-valued Weyl–Titchmarsh functions, we prove various trace ideal properties of powers of resolvent differences of ...
متن کاملar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions
متن کامل
ar X iv : 0 81 1 . 24 38 v 2 [ he p - ph ] 2 1 N ov 2 00 8 Theory Summary : International Symposium on Multiparticle Dynamics 2008
I summarize the theory talks presented at the International Symposium on Multiparticle Dynamics 2008.
متن کاملar X iv : 0 81 2 . 50 38 v 1 [ m at h . SP ] 3 0 D ec 2 00 8 SEMICLASSICAL ANALYSIS OF SCHRÖDINGER OPERATORS WITH MAGNETIC WELLS
We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schrödinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the individual eigenvalues for operators on closed manifolds and existence of gaps in intervals close to the bottom of the spectrum of periodic operators.
متن کامل