相关论文: Perturbation of Sectorial Projections of Elliptic …

A Calder\'on projector for an elliptic operator $P$ on a manifold with boundary $X$ is a projection from general boundary data to the set of boundary data of solutions $u$ of $Pu=0$. Seeley proved in 1966 that for compact $X$ and for $P$…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…

We consider a continuous family of linear elliptic differential operators of arbitrary order over a smooth compact manifold with boundary. Assuming constant dimension of the spaces of inner solutions, we prove that the orthogonalized…

An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with…

We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic…

In this first part of the paper, we define a natural dual object for manifolds with corners and show how pseudodifferential calculus on such manifolds can be constructed in terms of the localization principle in C*-algebras. In the second…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. Relying on a basis of pseudodifferential…

We investigate properties of pseudodifferential operators on $L^2$ space on manifold with ends including asymptotically conical or hyperbolic ends. Our pseudodifferential operators are a generalization of the canonical quantization which…

First, we review the Dirac operator folklore about basic analytic and geometrical properties of operators of Dirac type on compact manifolds with smooth boundary and on closed partitioned manifolds and show how these properties depend on…

The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…

We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex…

It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a…

This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior…

This article is about the (minimal) sector containing the numerical range of the principal part of a linear second-order elliptic differential operator defined by a form on closed subspaces V of the first-order Sobolev space…

This is a review of some coordinate-free calculi of pseudodifferential operators developed in the last years. As an application, we use a coordinate-free calculus to obtain new results on the behaviour of the spectral projections of a…

For every closed subset $X$ of a stratifiable [resp. metrizable] space $Y$ we construct a positive linear extension operator $T:R^{X\times X}\to R^{Y\times Y}$ preserving constant functions, bounded functions, continuous functions,…

One way to geometrically encode the singularities of a stratified pseudomanifold is to endow its interior with an iterated fibred cusp metric. For such a metric, we develop and study a pseudodifferential calculus generalizing the…

In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…

We consider a specific class of manifolds with singularities, namely, stratified manifolds, and describe a class of pseudodifferential operators (PsiDO) related to differential operators with degeneration of first-order with respect to the…

Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the…