3 citations · 14 across the 22 of their papers we have counts for
19 papers · 1 filter
A Shubin pseudodifferential calculus on asymptotically conic manifolds
Thomas Krainer
We present a global pseudodifferential calculus on asymptotically conic manifolds that generalizes (anisotropic versions of) Shubin's classical global pseudodifferential calculus o…
Cobordism invariance of the index for realizations of elliptic operators revisited
Thomas Krainer
We revisit an argument due to Lesch (Topology 32 (1993), no. 3, 611-623) for proving the cobordism invariance of the index of Dirac operators on even-dimensional closed manifolds a…
Extensions of symmetric operators that are invariant under scaling and applications to indicial operators
Thomas Krainer
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on gene…
Elliptic complexes of first-order cone operators: ideal boundary conditions
Thomas Krainer, Gerardo A. Mendoza
The purpose of this paper is to provide a detailed description of the spaces that can be specified as domains for the operators of a first order elliptic complex on a compact…
The Friedrichs extension for elliptic wedge operators of second order
Thomas Krainer, Gerardo A. Mendoza
The paper provides an explicit description of the structure of the domain of the Friedrichs extension of a second order semibounded elliptic wedge operator, initially defined on sm…
Boundary value problems for elliptic wedge operators: the first order case
Thomas Krainer, Gerardo A. Mendoza
This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material c…
A calculus of abstract edge pseudodifferential operators of type
Thomas Krainer
In this paper we expand on B.-W. Schulze's abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on Hörmander's calculus,…
Boundary value problems for first order elliptic wedge operators
Thomas Krainer, Gerardo A. Mendoza
We develop an elliptic theory based in of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum…
The kernel bundle of a holomorphic Fredholm family
Thomas Krainer, Gerardo A. Mendoza
Let $\Y$ be a smooth connected manifold, $Σ\subset\C$ an open set and $(σ,y)\to\scrP_y(σ)$ a family of unbounded Fredholm operators of index 0 depending smoot…
Elliptic systems of variable order
Thomas Krainer, Gerardo A. Mendoza
The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consi…
On the closure of elliptic wedge operators
Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza
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 expan…
Dynamics on Grassmannians and resolvents of cone operators
Juan Gil, Thomas Krainer, Gerardo Mendoza
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…
Maximal regularity for parabolic partial differential equations on manifolds with cylindrical ends
Thomas Krainer
We give a short, simple proof of maximal regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and…
A conic manifold perspective of elliptic operators on graphs
Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza
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…
R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators
Robert Denk, Thomas Krainer
It is shown that an elliptic scattering operator on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and P…
Elliptic boundary problems on manifolds with polycylindrical ends
Thomas Krainer
We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifo…
Resolvents of elliptic boundary problems on conic manifolds
Thomas Krainer
This paper is a continuation of the investigation of resolvents of elliptic operators on conic manifolds from math.AP/0410178 and math.AP/0410176 to the case of manifolds with boun…
Resolvents of elliptic cone operators
Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza
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 construct…
Geometry and spectra of closed extensions of elliptic cone operators
Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza
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 ne…