Related papers: Norm closure of classical pseudodifferential opera…

Let $G$ be a compact Lie group of dimension $n.$ In this work we characterise the membership of classical pseudo-differential operators on $G$ in the trace class ideal $S_{1}(L^2(G)),$ as well as in the setting of the Schatten ideals…

In this work we establish a subelliptic sharp G\r{a}rding inequality on compact Lie groups for pseudo-differential operators with symbols belonging to global subelliptic H\"ormander classes. In order for the inequality to hold we require…

In this paper, we study the boundedness of pseudo-differential operators with symbols in $S_{\rho,\delta}^m$ on the modulation spaces $M^{p,q}$. We discuss the order $m$ for the boundedness $\mathrm{Op}(S_{\rho,\delta}^m) \subset…

We consider a class of multiparameter singular Radon integral operators on the Heisenberg group ${\mathbb H}^1$ where the underlying variety is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg…

For a large class of semiclassical operators $P(h)-z$ which includes Schr\"odinger operators on manifolds with boundary, we construct the Quantum Monodromy operator $M(z)$ associated to a periodic orbit $\gamma$ of the classical flow. Using…

We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to $L^2$-compactness via a compact version of the $T(1)$ theorem.

In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y),…

In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…

In this paper, we will look at the algebra of global differential operators $D_X$ on wonderful compactifications $X$ of symmetric spaces $G/H$ of type $A_1$ and $A_2$. We will first construct a global differential operator on these…

In this work we obtain continuity results on H\"older spaces for operators belonging to a Weyl-H\"ormander calculus for metrics such that the class of the associated operators contains, in particular, certain hypoelliptic laplacians. With…

To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth…

Let $T^n$ denote the n-dimensional torus. The class of the bounded operators on $L^2(T^n)$ with analytic orbit under the action of $T^n$ by conjugation with the translation operators is shown to coincide with the class of the zero-order…

This paper demonstrates the stability of the global regularity for a class of pseudo-differential operators under lower-order perturbations. We establish that if an operator has a globally hypoelliptic symbol, its global regularity (in the…

We exhibit a Banach space $Z$ failing the approximation property, for which there is an uncountable family $\mathscr F$ of closed subideals contained in the Banach algebra $\mathcal K(Z)$ of the compact operators on $Z$, such that the…

We give a classification for connected complete locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Killing $L^{2}-$form. Moreover, we prove vanishing theorems…

Mixed-norm $\alpha$-modulation spaces were introduced recently by Cleanthous and Georgiadis [Trans.\ Amer.\ Math.\ Soc.\ 373 (2020), no. 5, 3323-3356]. The mixed-norm spaces $M^{s,\alpha}_{\vec{p},q}(\mathbb{R}^n)$, $\alpha\in [0,1]$, form…

We study some formality criteria for differential graded algebras over differential graded operads. This unifies and generalizes other known approaches like the ones by Manetti and Kaledin. In particular, we construct general operadic…

Beltran \& Cladek~\cite{BC} use $L^r$ to $L^s$ bounds to prove sparse form bounds for pseudodifferential operators with H\"ormander symbols in $S^m_{\rho,\delta}$ up to, but not including, the sharp end-point in decay $m$. We further…

The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the…

We provide evidence for the conjecture that the Wodzicki-Chern classes vanish for all bundles with the group Z of invertible zeroth order pseudodifferential operators as structure group. In particular, we prove this vanishing if the…