相关论文: A brief description of operators associated to the…
In this paper we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of $r$-nuclear operators on Lebesgue spaces.
In this paper we study multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of $r$-nuclear operators on Lebesgue spaces. We also study the nuclear trace and the spectral trace of these…
In this paper we prove H\"ormander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be extended to also obtain the $L^p$-boundedness results for…
We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some…
In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…
In this note we investigate some conditions of H\"ormander-Mihlin type in order to assure the $L^\infty$-${\textnormal{BMO}}$ boundedness for pseudo-multipliers of the harmonic oscillator. The $\textnormal{H}^1$-$L^1$ continuity for Hermite…
In this work we study a class of anharmonic oscillators on $\mathbb{R}^n$ corresponding to Hamiltonians of the form $A(D)+V(x)$, where $A(\xi)$ and $V(x)$ are $C^{\infty}$ functions enjoying some regularity conditions. Our class includes…
We consider operators acting on a UMD Banach lattice $X$ that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\frac12\Delta + \frac12|x|^{2} $ acting on…
We obtain a number of explicit estimates for quasi-norms of pseudo-differential operators in the Schatten-von Neumann classes $S_q$ with $0<q\le 1$. The estimates are applied to derive semi-classical bounds for operators with smooth or…
We establish continuity and Schatten-von Neumann properties for matrix operators with matrices satisfying mixed quasi-norm estimates. These considerations also include the case when the Lebesgue and Schatten parameters are allowed to stay…
Schur multipliers are basic linear maps on matrix algebras. Their close albeit still intriguing connection with Fourier multipliers establishes a powerful bridge between harmonic analysis and operator algebras. In this paper, we survey…
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…
This work addresses a ${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending…
In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting on the kernel. As…
This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator $\Delta_N$ on $\mathbb R^n$. Along the line of singular value estimates for Riesz transform commutators established by…
In this work we study a class of anharmonic oscillators within the framework of the Weyl-H\"ormander calculus. The anharmonic oscillators arise from several applications in mathematical physics as natural extensions of the harmonic…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x…
In this paper we introduce the Schatten class of operators and the Berezin transform of operators in the quaternionic setting. The first topic is of great importance in operator theory but it is also necessary to study the second one…
In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional…