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We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x −ν Diff m b 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.

- Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza
- 2005

We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.

We study the geometry of the set of closed extensions of index 0 of an elliptic differential 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.

- Gerardo A. Mendoza, T. Krainer
- 2012

This talk reflects work in progress with T. Krainer directed at studying elliptic boundary value problems in a context well beyond the classical set-up. LetM be a smooth noncompact manifold, or just an open set in some euclidean space. Let μ be a smooth density on M and P an elliptic linear partial differential operator on M with smooth coefficients. The… (More)

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.

We analyze the behavior of the trace of the resolvent of an ellip-tic 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… (More)

- G A Mendoza, N Sprunk, +5 authors A Knoll
- Conference proceedings : ... Annual International…
- 2011

For patients suffering from cardiogenic shock cardiopulmonary resuscitation may not be sufficient to restore normal heart function. However, their chances of survival may be increased with the use of an extracorporeal support system. With this system the patient's organs are perfused while being transported to the nearest hospital for proper treatment. In… (More)

The paper proves the existence and elucidates the structure of the asymptotic expansion of the trace of the resolvent of a closed extension of a general elliptic cone operator on a compact manifold with boundary as the spectral parameter tends to infinity. The hypotheses involve only minimal conditions on the symbols of the operator. The results combine… (More)

We give a simple, explicit, sufficient condition for the existence of a sector of minimal growth for second order regular singular differential operators on graphs. We specifically consider operators with a singular potential of Coulomb type and base our analysis on the theory of elliptic cone operators.

We analyze the behavior of the trace of the resolvent of an ellip-tic 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… (More)