Weighted Estimates for Toeplitz Operators Related to Pseudodifferential Operators
Journal of Function Spaces, 2016 The authors establish the weighted Lp estimates for a class of pseudodifferential operators for both cases ...
Yan Lin +3 more
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$L^{p}$ estimates for joint quasimodes of semiclassical pseudodifferential operators
Israel Journal of Mathematics, 2018 We develop a set of $L^{p}$ estimates for functions $u$ that are a joint quasimode (approximate eigenfunction) of $r$ pseudodifferential operators $p_{1}(x,hD),\dots,p_{r}(x,hD)$. This work extends Sarnak and Marshall's work on symmetric space to cover a
Tacy, Melissa
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Pseudodifferential operators on filtered manifolds as generalized fixed points [PDF]
Journal of Noncommutative Geometry, 2021 On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour.
Eske Ewert
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Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators [PDF]
Journal of Pseudo-Differential Operators and Applications, 2022 We generalize the results for Banach algebras of pseudodifferential operators obtained by Gröchenig and Rzeszotnik (Ann Inst Fourier 58:2279–2314, 2008) to quasi-algebras of Fourier integral operators. Namely, we introduce quasi-Banach algebras of symbol
E. Cordero, Gianluca Giacchi
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Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography [PDF]
SIAM Journal of Imaging Sciences, 2020 We propose a novel convolutional neural network (CNN), called $\Psi$DONet, designed for learning pseudodifferential operators ($\Psi$DOs) in the context of linear inverse problems. Our starting point is the Iterative Soft Thresholding Algorithm (ISTA), a
T. Bubba +5 more
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Viscosity Limits for Zeroth‐Order Pseudodifferential Operators
Communications on Pure and Applied Mathematics, 2022 Motivated by the work of Colin de Verdière and Saint‐Raymond on spectral theory for zeroth‐order pseudodifferential operators on tori, we consider viscosity limits in which zeroth‐order operators, P, are replaced by P + iν Δ, ν > 0.
J. Galkowski, M. Zworski
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Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case [PDF]
Partial Differential Equations, Spectral Theory, and Mathematical Physics, 2020 In a domain $\Omega\subset \mathbb{R}^{\mathbf{N}}$ we consider a selfadjoint operator $\mathbf{T}=\mathfrak{A}^*P\mathfrak{A} ,$ where $\mathfrak{A}$ is a pseudodifferential operator of order $-l=-\mathbf{N}/2$ and $P=V\mu_{\Sigma}$ is a singular signed
G. Rozenblum, E. Shargorodsky
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Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime [PDF]
, 2020 We obtain new semiclassical estimates for pseudodifferential operators with low regular symbols. Such symbols appear naturally in a Cauchy Problem related to recent weak solutions to the unstable Muskat problem constructed via convex integration.
V'ictor Arnaiz, A. Castro, Daniel Faraco
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Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions [PDF]
RACSAM, 2019 We develop a theory of pseudodifferential operators of infinite order for the global classes Sω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Vicente Asensio, David Jornet
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The scattering matrix for 0th order pseudodifferential operators [PDF]
Annales de l'Institut Fourier, 2019 We use microlocal radial estimates to prove the full limiting absorption principle for $P$, a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions as of Colin de Verdi\`ere and Saint-Raymond.
Jian Wang
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