Related papers: Schatten-von Neumann properties for H\"ormander cl…

Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. We show that its $C^*$-closure is an extension of a noncommutative algebra of principal…

In this note we present criteria on both symbols and integral kernels ensuring that the corresponding operators on compact manifolds belong to Schatten classes. A specific test for nuclearity is established as well as the corresponding…

We generalize our results of \cite{AP2} and \cite{AP3} to the case of maximal dissipative operators. We obtain sharp conditions on a function analytic in the upper half-plane to be operator Lipschitz. We also show that a H\"older function…

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…

We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as a zero-order perturbation of a sum of squares of vector fields with real-analytic coefficients on compact Lie groups. The key…

We characterize the Schatten class Toeplitz operators induced by a positive Borel measure on the unit disc and the reproducing kernel of the Bergman space $A^2_\omega$, where $\omega$ is a radial weight satisfying the doubling property…

We define classes of pseudodifferential operators on $G$-bundles with compact base and give a generalized $L^2$ Fredholm theory for invariant operators in these classes in terms of von Neumann's $G$-dimension. We combine this formalism with…

We prove three results giving sufficient and/or necessary conditions for discreteness of the spectrum of Schr\"odinger operators with non-negative matrix-valued potentials, i.e., operators acting on $\psi\in L^2(\mathbb{R}^n,\mathbb{C}^d)$…

A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…

We discuss some of the analytic properties of lens space indices for 4d N=2 theories of class S. The S-duality properties of these theories highly constrain the lens space indices, and imply in particular that they are naturally acted upon…

We identify Melrose's suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space $\R$. For a general algebra of parametric pseudodifferential operators,…

We generalize some results on compact operators on Hilbert spaces to "compact" operators on some Hilbert right W*-modules. We present in this frame the Schatten decomposition of the compact operators, the trace, the Banach Lp-spaces and…

This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of…

We consider bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class, $BS_{\rho, \rho}^m$, $m \in \mathbb{R}$, $0 \leq \rho < 1$. The aim of this paper is to discuss low regularity conditions for symbols to…

This paper has been withdrawn by the authors. A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those…

Let $G_\C$ be a connected, linear algebraic group defined over $\R$, acting regularly on a finite dimensional vector space $V_\C$ over $\C$ with $\R$-structure $V_\R$. Assume that $V_\C$ posseses a Zariski-dense orbit, so that…

We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The…

Let $M = \Gamma \setminus \mathbb{H}_d$ be a compact quotient of the $d$-dimensional Heisenberg group $\mathbb{H}_d$ by a lattice subgroup $\Gamma$. We give Schatten and Sobolev estimates for the Green operator $\mathcal{G}_\alpha$…

We consider harmonic Toeplitz operators $T_V = PV:{\mathcal H}(\Omega) \to {\mathcal H}(\Omega)$ where $P: L^2(\Omega) \to {\mathcal H}(\Omega)$ is the orthogonal projection onto ${\mathcal H}(\Omega) = \left\{u \in L^2(\Omega)\,|\,\Delta u…

For a bounded quaternionic operator $T$ on a right quaternionic Hilbert space $\mathcal{H}$ and $\varepsilon >0$, the pseudo $S$-spectrum of $T$ is defined as \begin{align*} \Lambda_{\varepsilon}^{S}(T) := \sigma_S (T) \bigcup \left \{ q…