Related papers: Characterization of Non-Smooth Pseudodifferential …

We show that an elliptic uniform pseudodifferential operator over a manifold of bounded geometry defines a class in uniform K-homology, and that this class only depends on the principal symbol of the operator.

In this paper, the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2 \times L^2$ are determined in the framework of Besov spaces. Our result improves the $L^2 \times L^2 \to L^1$ boundedness of those operators with…

We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.

This dissertation concerns the pseudo-differential operators of type 1,1. These have been known especially since around 1980, when it was shown that they play an important role in the treatment of fully non-linear partial differential…

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…

We study the holomorphic extendibility of $\text{Op}(p)u$, when $p$ is an analytic symbol, and explicit information is available on the domains of holomorphic extendibility of both $p$ and $u$. By a contour deformation argument, we obtain a…

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…

The Weyl symbolic calculus of operators leads to the construction, if one takes for symbol a certain distribution decomposing over the zeros of the Riemann zeta function, of an operator with the following property: the Riemann hypothesis is…

First, we reconsider the magnetic pseudodifferential calculus and show that for a large class of non-decaying symbols, their corresponding magnetic pseudodifferential operators can be represented, up to a global gauge transform, as…

We consider the problem of identifying a linear deterministic operator from its response to a given probing signal. For a large class of linear operators, we show that stable identifiability is possible if the total support area of the…

We investigate global microlocal properties of localization operators and Shubin pseudodifferential operators. The microlocal regularity is measured in terms of a scale of Shubin-type Sobolev spaces. In particular, we prove microlocality…

Let us consider the set S^A(\R^n) of rapidly decreasing functions G:\R^n \to A, where A is a separable C^*-algebra. We prove a version of the Calder\'on-Vaillancourt theorem for pseudodifferential operators acting on S^A(\R^n) whose symbol…

In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…

Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s>d/\min{(1,p,q)}-d$ for $0<p<\infty$, and from $B_p^{s+m,q}$ to $B_{p}^{s,q}$ if $s>d/\min{(1,p)}-d$ for $0<p\leq\infty$. In…

We characterize $k-$smoothness of an element on the unit sphere of a finite-dimensional polyhedral Banach space. Then we study $k-$smoothness of an operator $T \in \mathbb{L}(\ell_{\infty}^n,\mathbb{Y}),$ where $\mathbb{Y}$ is a…

In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its…

In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel-Lizorkin-type spaces with variable exponents $B^{\mathrm{\boldsymbol{\omega}}, \phi}_{p(\cdot),q(\cdot)}(\mathbb{R}^n)$ and…

This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space $x$ and frequency $\xi$. The symbol smoothness conditions obeyed by many…