q 伯格曼空间上的托普利兹算子和组成算子

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Pseudo-Differential Operators and Applications Pub Date : 2024-02-10 DOI:10.1007/s11868-023-00583-x

Houcine Sadraoui, Borhen Halouani

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引用次数: 0

摘要

在这项研究中，我们考虑了 q-Bergman 空间上的托普利兹算子和组成算子。我们给出了一般托普利兹算子的一些谱性质，并给出了在符号的解析部分是单项式的情况下托普利兹算子下规范性的充分条件。我们还给出了谐符号一般情况下下规范性的必要条件，以及此类算子换向的必要条件和充分条件。对于组成算子，我们给出了其紧凑性和正态性的必要条件和充分条件，以及线性分数映射情况下的共正态性的必要条件，最后我们计算了线性映射情况下的邻接算子。

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Toeplitz operators and composition operators on the q-Bergman space

In this work we consider Toeplitz operators and composition operators on the q-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition for hyponormality of Toeplitz operators in the case of a symbol where the analytic part is a monomial. We also give a necessary condition for hyponormality in the general case of a harmonic symbol as well as a necessary and sufficient condition for such operators to commute. For composition operators we give necessary conditions and sufficient conditions for their compactness and normality, as well as necessary conditions for cohyponormality in the case of a linear fractional map and we finally compute the adjoint in the case of a linear map.

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来源期刊

Journal of Pseudo-Differential Operators and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.20

自引率

9.10%

发文量

期刊介绍： The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.