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Related papers: Endpoint Schatten class properties of commutators

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This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in (\ell^{2,p}), then…

Functional Analysis · Mathematics 2009-08-26 Shannon Bishop

We investigate a class of spectral multipliers for an Ornstein-Uhlenbeck operator $\mathcal L$ in $\mathbb R^n$, with drift given by a real matrix $B$ whose eigenvalues have negative real parts. We prove that if $m$ is a function of Laplace…

Functional Analysis · Mathematics 2023-09-28 Valentina Casarino , Paolo Ciatti , Peter Sjögren

In this work we investigate a class of degenerate Schr\"odinger equations associated to degenerate elliptic operators with irregular potentials on $\Ran$ by introducing a suitable H\"ormander metric $g$ and a $g$-weight $m$. We establish…

Analysis of PDEs · Mathematics 2023-02-07 Duván Cardona , Marianna Chatzakou , Julio Delgado , Michael Ruzhansky

We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten type classes are obtained. Some upper asymptotic estimates for…

Functional Analysis · Mathematics 2017-09-01 Elena P. Ushakova

In this paper we deal with a second order multidimensional fractional differential operator. We consider a case where the leading term represented by the uniformly elliptic operator and the final term is the Kipriyanov operator of…

Functional Analysis · Mathematics 2020-02-06 M. V. Kukushkin

In this note we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to Schatten classes on $L^2(\mathbb{R}^n)$. We also investigate the spectral trace of these operators.

Functional Analysis · Mathematics 2018-03-22 Duvan Cardona

In this paper, a discrete form of the Kato inequality for discrete magnetic Laplacians on graphs is used to study asymptotic properties of the spectrum of discrete magnetic Schrodinger operators. We use the existence of a ground state with…

Spectral Theory · Mathematics 2007-05-23 Jozef Dodziuk , Varghese Mathai

We determine the Schatten class for the compact resolvent of Dirichlet realizations, in unbounded domains, of a class of non-selfadjoint differential operators. This class consists of operators that can be obtained via analytic dilation…

Mathematical Physics · Physics 2014-10-21 Yaniv Almog , Bernard Helffer

We have studied the complete set of dimension 5 and dimension 6 effective operators involving the interaction of scalar, fermion and vector Dark Matter (DM) with SM quarks and gluons, to explore the possibility to distinguish these…

High Energy Physics - Phenomenology · Physics 2017-05-24 Alexander Belyaev , Luca Panizzi , Alexander Pukhov , Marc Thomas

We characterize the Schatten class membership of the canonical solution operator to $\bar\partial$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in…

Complex Variables · Mathematics 2011-01-13 Olivia Constantin , Joaquim Ortega-Cerdà

A full description of the membership in the Schatten ideal $S_ p(A^2_{\omega})$ for $0<p<\infty$ of the Toeplitz operator acting on large weighted Bergman spaces is obtained.

Functional Analysis · Mathematics 2015-09-07 Hicham Arroussi , Inyoung Park , Jordi Pau

We consider norms on a complex separable Hilbert space such that $\langle a\xi,\xi\rangle\leq\|\xi\|^2\leq\langle b\xi,\xi\rangle$ for positive invertible operators $a$ and $b$ that differ by an operator in the Schatten class. We prove that…

Functional Analysis · Mathematics 2020-02-21 Martin Miglioli

Commutator relations are used to investigate the spectra of Schr\"odinger Hamiltonians, $H = -\Delta + V({x}),$ acting on functions of a smooth, compact $d$-dimensional manifold $M$ immersed in $\bbr^{\nu}, \nu \geq d+1$. Here $\Delta$…

Spectral Theory · Mathematics 2007-05-23 Evans M. Harrell

In this paper, we consider the restricted $p$-Schatten class Grassmannian $\mathrm {Gr}_{{\rm res}, p}(\mathcal{H})$ consisting of infinite-dimensional and infinite codimensional subspaces $W$ of a polarized complex separable Hilbert space…

Functional Analysis · Mathematics 2026-05-22 Amin Tahiri , Alice Barbora Tumpach

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex optimization over spaces of tensors is now gaining much interest…

Optimization and Control · Mathematics 2016-07-01 Stéphane Chrétien , Tianwen Wei

We consider a second order difference equation with operator-valued coefficients. More precisely, we study either compact or trace class perturbations of the discrete Laplacian in the Hilbert space of bi-infinite square-summable sequence…

Spectral Theory · Mathematics 2025-01-22 David Sher , Luis Silva , Boris Vertman , Monika Winklmeier

This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…

Probability · Mathematics 2025-03-03 Qi Hou , Laurent Saloff-Coste

Motivated by the problem of understanding theoretical bounds for the performance of the Belkin-Niyogi Laplacian eigencoordinate approach to dimension reduction in machine learning problems, we consider the convergence of random graph…

Functional Analysis · Mathematics 2025-03-10 Bernard Akwei , Luke Rogers , Alexander Teplyaev

For a normal measurable operator $a$ affiliated with a von Neumann factor $\mathcal{M}$ we show: If $\mathcal{M}$ is infinite, then there is $\lambda_0\in \mathbb{C}$ so that for $\varepsilon>0$ there are…

Operator Algebras · Mathematics 2023-04-24 Alexei Ber , Matthijs Borst , Fedor Sukochev

We study Schatten--von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of $L^\infty$ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten--von Neumann…

Functional Analysis · Mathematics 2017-06-07 Alexei Aleksandrov , Vladimir Peller