Related papers: Fibered Cusp b-Pseudodifferential Operators and it…

This article describes a class of pseudo-differential operators \begin{equation*} (\mathcal{A}^{\alpha}\varphi)(x)=\mathcal{F}^{-1}_{\xi \rightarrow…

In this paper we present a formula for the index of a pseudodifferential operator with invertible principal symbol in the extended Heisenberg calculus of Epstein and Melrose. Our results build on the work we did in a previous paper…

Given a semistable fibration $f\colon X\to B$ we introduce a correspondence between foliations $\mathcal{F}$ on $X$ and local systems $\mathbb{L}$ on $B$. Building up on this correspondence we find conditions that give maximal rationally…

We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional "rough" signals, i.e. "differentials" of given H\"older…

Let M be a compact manifold of dimension n, P = P(h) a semiclassical pseudodifferential operator on M, and u = u(h) an L^2 normalised family of functions such that Pu is O(h) in L^2(M) as h goes to 0. Let H be a compact submanifold of M. In…

We prove some Fredholm conditions for many algebras of differential operators on particular classes of open manifolds, which include asymptotically Euclidean or asymptotically hyperbolic manifolds. Our typical result is that an operator $P$…

Spectral sections of families of self-adjoint Fredholm operators were introduced by Melrose and Piazza for the needs of index theory. The basic result about spectral sections is a theorem of Melrose and Piazza to the effect that a family…

We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate…

We consider a Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M,g)$ with a nonempty boundary. The operator $D_P$ is specified by a boundary condition $P(u|_{\p M})=0$ where $P$ is a projector which may…

A manifold with fibered cusp metrics $X$ can be considered as a geometrical generalization of locally symmetric spaces of $\mathbb{Q}$-rank one at infinity. We prove a Hodge-type theorem for this class of Riemannian manifolds, i.e. we find…

We define here a pseudo B-Fredholm operator as an operator such that 0 is isolated in its essential spectrum, then we prove that an operator $T$ is pseudo- B-Fredholm if and only if $T = R + F$ where $R$ is a Riesz operator and $F$ is a…

We give a self-contained proof of a formula computing the Fredholm index for asymptotically non-degenerate Cauchy-Riemann operators on surfaces with boundary punctures using the method of large antilinear deformations. This method for…

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed aspherical manifold, we show that T gives…

We construct the Calderon projection on the space of Cauchy datas for a twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus for operators acting on bundles of finitely generated $C^*$--Hilbert modules on a compact…

This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…

We give a cohomological formula for the index of a fully elliptic pseudodifferential operator on a manifold with boundary. As in the classic case of Atiyah-Singer, we use an embedding into an euclidean space to express the index as the…

Applying the Fedosov connections constructed in our previous work, we find a (dense) subsheaf of smooth functions on a K\"ahler manifold $X$ which admits a non-formal deformation quantization. When $X$ is prequantizable and the Fedosov…

In this work, we develop $L^p$ boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the $x$ variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in terms of scale…

We present a condition for towers of fiber bundles which implies that the fundamental group of the total space has a nilpotent subgroup of finite index whose torsion is contained in its center. Moreover, the index of the subgroup can be…

We study the gap (= "projection norm" = "graph distance") topology of the space of (not necessarily bounded) self--adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show…