Related papers: Rigidity of differential operators and Chern numbe…
We consider a strongly elliptic differential expression of the form $b(D)^* g(x/\varepsilon) b(D)$, $\varepsilon >0$, where $g(x)$ is a matrix-valued function in ${\mathbb R}^d$ assumed to be bounded, positive definite and periodic with…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
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…
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses and on the regularity of the solutions to the associated…
We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for…
We consider smooth vector bundles over smooth manifolds equipped with non-smooth geometric data. For nilpotent differential operators acting on these bundles, we show that the kernels of induced Hodge-Dirac-type operators remain isomorphic…
We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms…
We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral…
For this quarter of century, differential operators in a lower dimensional submanifold embedded or immersed in real $n$-dimensional euclidean space $\EE^n$ have been studied as quantum mechanical models, which are realized as restriction of…
We prove an index theorem for families of pseudodifferential operators generalizing those studied by C. Callias, N. Anghel and others. Specifically, we consider operators on a manifold with boundary equipped with an asymptotically conic…
We prove a differential analogue of Hilbert's irreducibility theorem. Let $\mathcal{L}$ be a linear differential operator with coefficients in $C(\mathbb{X})(x)$ that is irreducible over $\overline{C(\mathbb{X})}(x)$, where $\mathbb{X}$ is…
We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…
The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown…
We present spectrally disjoint Sidon automorphisms whose tensor squares are isomorphic to a planar shift. Spectra of such automorphisms do not possess the group property. To check the singularity of spectrum, we use polynomial rigidity of…
If a differential operator $D$ on a smooth Hermitian vector bundle $S$ over a compact manifold $M$ is symmetric, it is essentially self-adjoint and so admits the use of functional calculus. If $D$ is also elliptic, then the Hilbert space of…
The classical multiplicative (Hirzebruch) genera of manifolds have the wonderful property which is called rigidity. Rigidity of a genus h means that if a compact connected Lie group G acts on a manifold X, then the equivariant genus h^G(X)…
We study $L^p$-theory of second-order elliptic divergence type operators with complex measurable coefficients. The major aspect is that we allow complex coefficients in the main part of the operator, too. We investigate generation of…
We consider the problem of the strong unique continuation for an elasticity system with general residual stress. Due to the known counterexamples, we assume the coefficients of the elasticity system are in the Gevrey class of appropriate…
This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in $n$-dimensional euclidean space $\EE^n$ to a surface or a space curve as physical…
The aim of this paper is to give strict fixed point principles for multivalued operators $T:X\rightarrow P(X)$ satisfying some contraction conditions of \'Ciri\' c and of \'Ciri\' c-Reich-Rus type. We are interested, under which conditions,…