Related papers: Index formulas on stratified manifolds

We prove that the index formula for $b$-elliptic cone differential operators given by M. Lesch holds verbatim for operators whose coefficients are not necessarily independent of the normal variable near the boundary. We also show that, for…

We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces.…

In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.

A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold $M$ described by a $t$-dependent vector field $X=\sum_{\alpha=1}^rg_\alpha X_\alpha$, where $X_1,\ldots,X_r$ are vector fields on…

We define the Laplacian operator on finite multicomplexes and give a formula for its spectra in the case of shifted multicomplexes.

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of…

We define certain class of correspondences of polarized representations of $C^*$-algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the…

In 1996, Berline and Vergne gave a cohomological formula for the index of a transversally elliptic operator. In this paper we propose a new point of view where the cohomological formulae make use of equivariant Chern characters with…

Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…

We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…

We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an…

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…

We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…

We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…

We consider a family of integral operators which appears when analyzing layered equilibria and front dynamics of a phase kinetics equation with a conservation law. We study the spectra of these operators in $L^2$ and derive a lower bound…

For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators `acting on sections of the projective bundle' in a formal…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

We demonstrate a method of associating the principal symbol at a $K$-point with a linear differential operator acting between modules over a commutative algebra, and we use it to define the ellipticity of a linear differential operator in a…

We determine the cd-index of the induced subdivision arising from a manifold arrangement. This generalizes earlier results in several directions: (i) One can work with manifolds other than the n-sphere and n-torus, (ii) the induced…

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to…