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This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…

Functional Analysis · Mathematics 2018-04-17 Xiang Fang , Kunyu Guo , Zipeng Wang

We consider a class of pseudodifferential operators defined on the product of two closed manifolds, with crossed vector valued symbols. We study the asymptotic expansion of Weyl counting function of positive selfadjoint operators in this…

Spectral Theory · Mathematics 2012-01-13 Ubertino Battisti

We study pseudodifferential operators associated to microlocally defined normed symbol spaces of limited regularity, introduced by J. Sj\"ostrand. Boundedness of such operators on modulation spaces is obtained under suitable conditions, and…

Functional Analysis · Mathematics 2025-06-17 Michael Hitrik , Reid Johnson

Poincare Polynomial of a Kac-Moody Lie algebra can be obtained by classifying the Weyl orbit $W(\rho)$ of its Weyl vector $\rho$. A remarkable fact for Affine Lie algebras is that the number of elements of $W(\rho)$ is finite at each and…

Mathematical Physics · Physics 2010-09-20 M. Gungormez , H. R. Karadayi

We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\eta)$ are elements of $C^{r}_{*}S^{m}_{1,\delta}$ classes that have limited regularity in the…

Analysis of PDEs · Mathematics 2023-08-09 Jan Rozendaal

Classical pseudo-differential calculus on $\mathbb{R}^{d}$ can be viewed as a (non-commutative) functional calculus for the standard position and momentum operators $(Q_{1}, \dots , Q_{d})$ and $(P_{1}, \dots , P_{d})$. We generalise this…

Functional Analysis · Mathematics 2018-06-05 Jan van Neerven , Pierre Portal

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given…

Mathematical Physics · Physics 2009-10-30 J. Bertrand , P. Bertrand

We deduce one-parameter group properties for pseudo-differential operators $\operatorname{Op} (a)$, where $a$ belongs to the class $\Gamma ^{(\omega _0)}_*$ of certain Gevrey symbols. We use this to show that there are pseudo-differential…

Functional Analysis · Mathematics 2017-12-13 Ahmed Abdeljawad , Sandro Coriasco , Joachim Toft

In this work, we introduce a global theory of subelliptic pseudo-differential operators on arbitrary homogeneous vector bundles over orientable compact homogeneous manifolds. We will show that a global pseudo-differential calculus can be…

Analysis of PDEs · Mathematics 2024-03-15 Duván Cardona , Vishvesh Kumar , Michael Ruzhansky

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,…

Functional Analysis · Mathematics 2007-05-23 Matthias Lesch , Markus J. Pflaum

We obtain improved bounds for pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\eta)$ are elements of $C^{r}_{*}S^{m}_{1,\delta}$ classes that have limited regularity in the…

Analysis of PDEs · Mathematics 2022-09-30 Jan Rozendaal

In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators $P_a$ of order $2a$, with type and factorization index $a\in R_+$, restricted to compact sets with boundary; this includes…

Analysis of PDEs · Mathematics 2014-11-04 Gerd Grubb

Given a separable unital C*-algebra A, let E denote the Banach-space completion of the A-valued Schwartz space on Rn with norm induced by the A-valued inner product $<f,g>=\int f(x)^*g(x) dx$. The assignment of the pseudodifferential…

Operator Algebras · Mathematics 2008-12-23 Severino T. Melo , Marcela I. Merklen

Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we…

Quantum Physics · Physics 2022-10-19 Maurice de Gosson

The main aim of the paper is Fredholm properties of a class of bounded linear operators acting on weighted Lebesgue spaces on an infinite metric graph $\Gamma$ which is periodic with respect to the action of the group ${\mathbb Z}^n$. The…

Functional Analysis · Mathematics 2011-07-27 Vladimir S. Rabinovich , Steffen Roch

In this thesis, we study singular pseudo-differential operators defined by groupoids satisfying the Lauter-Nistor condition, by a method parallel to that of manifolds with boundary and edge differential operators. The example of the Bruhat…

Analysis of PDEs · Mathematics 2010-06-30 Bing Kwan So

Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…

Functional Analysis · Mathematics 2016-10-17 Jan Stochel , Jerzy B. Stochel

The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consider vector bundles over the boundary together with general…

Analysis of PDEs · Mathematics 2013-07-11 Thomas Krainer , Gerardo A. Mendoza

In this paper we introduce conformally covariant boundary operators for Poincar\'e-Einstein manifolds satisfying a mild spectral assumption. Using these boundary operators we set up higher order Dirichlet problems whose solutions are such…

Differential Geometry · Mathematics 2023-11-17 Joshua Flynn , Guozhen Lu , Qiaohua Yang

In this paper we study the action of pseudo-differential operators acting on Gevrey spaces. We introduce classes of classical symbols with spatial Gevrey regularity. As the spatial Gevrey regularity of a symbol $p(\cdot,\xi)$ may depend on…

Analysis of PDEs · Mathematics 2017-09-11 Baptiste Morisse