Adjoints of elliptic cone operators

We study the adjointness problem for the closed extensions of a general b-elliptic operator A in x^{-\nu}Diff^m_b(M;E), \nu>0, initially defined as an unbounded operator A:C_c^\infty(M;E)\subset x^\mu L^2_b(M;E)\to x^\mu L^2_b(M;E), \mu \in \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.Comment: 40 pages, LaTeX, preliminary versio

Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.Comment: 30 pages, 5 figure

On the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds

Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of the trace \Tr Pe^{-tA}, where $A$ is an elliptic cone differential operator for which the resolvent exists on a suitable region of the complex plane. Our expansion contains $\log t$ and new $(\log t)^2$ terms whose coefficients are given explicitly by means of residue traces. Cone operators are contained in some natural algebras of pseudodifferential operators on which unique trace functionals can be defined. As a consequence of our explicit heat trace expansion, we recover all these trace functionals.Comment: 15 page

On the closure of elliptic wedge operators

We prove a semi-Fredholm theorem for the minimal extension of elliptic operators on manifolds with wedge singularities and give, under suitable assumptions, a full asymptotic expansion of the trace of the resolvent.Comment: 22 pages, improved expositio

Resolvents 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.Comment: 46 pages, submitted for publicatio

Trace expansions for elliptic cone operators with stationary domains

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.Comment: 27 pages. Minor corrections and change of titl

Geometry and spectra of closed extensions of elliptic cone operators

We study the geometry of the set of closed extensions of index 0 of an elliptic cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.Comment: 48 pages, revisited version to appear in Canadian Journal of Mathematic

Unemployment hysteresis, structural changes, non-linearities and fractional integration in Central and Eastern Europe

In this paper we aim to analyse the dynamics of unemployment in a group of Central and Eastern European Countries (CEECs). The CEECs are of special importance for the future of the European Union, given that most of them have recently become member states, and labour flows have been seen to rise with their accession. By means of unit root tests incorporating structural changes and nonlinearities, as well as fractional integration, we find that the unemployment rates for the CEECs are mean reverting processes, which is consistent with the NAIRU hypothesis, although shocks tend to be highly persistent.Unemployment, NAIRU, hysteresis, unit roots, fractional integration