Related papers: Index of nonlocal elliptic boundary value problems…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…
The aim of this article is to analyze the asymptotic behaviour of the eigenvalues of elliptic operators in divergence form with mixed boundary type conditions for domains that become unbounded in several directions, while they stay bounded…
We pursue the study of local index theory for operators of Fourier-integral type associated to non-proper and non-isometric actions of Lie groupoids, initiated in a previous work. We introduce the notion of geometric cocycles for Lie…
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…
We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators…
We study boundary conditions for elliptic operators on non-compact manifolds with boundary via uniform K-homology, a version of K-homology sensitive to the large-scale geometry of the manifold. To that end, we develop the theory of relative…
We study the index of the $G$-invariant elliptic pseudo-differential operator acting on a complete Riemannian manifold, where a unimodular, locally compact group $G$ acts properly and cocompactly. An $L^2$-index formula was obtained using…
We prove index formulas for elliptic operators acting between sections of C*-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C*-algebra to de Rham homology of smooth subalgebras. We…
We develop elliptic theory of operators associated with a diffeomorphism of a closed smooth manifold. The aim of the present paper is to obtain an index formula for such operators in terms of topological invariants of the manifold and of…
We introduce a new class of natural, explicitly defined, transversally elliptic differential operators over manifolds with compact group actions. Under certain assumptions, the symbols of these operators generate all the possible values of…
We develop a formula for the equivariant index of a twisted Dirac operator on a compact globally hyperbolic spacetime with timelike boundary on which a group acts isometrically, subject to APS boundary conditions. The formula is the same as…
An analytic index is defined for a family of cusp pseudodifferential operators, $P_b,$ on a fibration with fibres which are compact manifolds with boundaries, provided the family is elliptic and has invertible indicial family at the…
In mid 60s Bott proved that (1) the index theorem for homogeneous, G-invariant, elliptic differential operators acting in the spaces of sections of induced representations of G over G/H reduces to the Weyl character formula and (2) the…
Index theory for Lorentzian Dirac operators is a young subject with significant differences to elliptic index theory. It is based on microlocal analysis instead of standard elliptic theory and one of the main features is that a nontrivial…
In this paper, an equality between the Hochs-Mathai type index and the Atiyah-Patodi-Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group…
We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of…
Many index theorems (both classical and in noncommutative geometry) can be interpreted in terms of a Lie groupoid acting properly on a manifold and leaving an elliptic family of pseudodifferential operators invariant. Alain Connes in his…
Many index theorems (both classical and in noncommutative geometry) can be interpreted in terms of a Lie groupoid acting properly on a manifold and leaving an elliptic family of pseudodifferential operators invariant. Alain Connes in his…
We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone…