相关论文: Equivariant Brill-Noether theory for elliptic oper…

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…

We study the index theory of hypoelliptic operators on Carnot manifolds -- manifolds whose Lie algebra of vector fields is equipped with a filtration induced from sub-bundles of the tangent bundle. A Heisenberg pseudodifferential operator,…

This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…

Motivated by the dynamics of defects in planar pattern-forming systems, we study Fredholm properties of elliptic operators with singular coefficients in weighted Sobolev spaces. In particular, we consider a family of doubly weighted spaces…

We classify non-linear proper Fredholm maps between Hilbert spaces, up to proper homotopy, in terms of the stable homotopy groups of spheres. We show that there is a surjective map from the stable homotopy groups of spheres to the set of…

We give explicit Fredholm conditions for classes of pseudodifferential operators on suitable singular and non-compact spaces. In particular, we include a "user's guide" to Fredholm conditions on particular classes of manifolds including…

This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvent, and their subspaces consisting of self-adjoint operators. Our main results are the…

We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product H\"ormander spaces parametrized with a real number and a function varying slowly at infinity in the sense…

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered…

Just as a symmetric surface with separating fixed locus halves into two oriented bordered surfaces, an arbitrary symmetric surface halves into two oriented symmetric half-surfaces, i.e. surfaces with crosscaps. Motivated in part by the…

We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic,…

Let $\Y$ be a smooth connected manifold, $\Sigma\subset\C$ an open set and $(\sigma,y)\to\scrP_y(\sigma)$ a family of unbounded Fredholm operators $D\subset H_1\to H_2$ of index 0 depending smoothly on $(y,\sigma)\in \Y\times \Sigma$ and…

We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator,…

We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and…

Let $M$ be a complex manifold with boundary $X$, which admits a holomorphic Lie group $G$-action preserving $X$. We establish a full asymptotic expansion for the $G$-invariant Bergman kernel under certain assumptions. As an application, we…

This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize…

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…

We study the Fredholm properties of a general class of elliptic differential operators on $\R^n$. These results are expressed in terms of a class of weighted function spaces, which can be locally modeled on a wide variety of standard…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses…