Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators

ar 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 ...

AbstractAbstr GRAPH SUBSPACES AND THE SPECTRAL SHIFT FUNCTION

We extend the concept of Lifshits–Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of (admissible) operators that are similar to self-adjoint operators. An operator H is called admissible if: (i) there is a bounded operator V with a bounded inverse such that H = V −1 HV for some self-adjoint operator H; (ii) the operators H and H are resolvent ...

Full 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...

On Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators