非负数阶的 Fock-Sobolev 空间上 Toeplitz 算子的半通约数

IF 0.7 4区数学 Q2 MATHEMATICS Complex Analysis and Operator Theory Pub Date : 2024-08-05 DOI:10.1007/s11785-024-01574-6

Jie Qin

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引用次数: 0

摘要

我们在描述非负阶的福克-索博廖夫空间上的托普利兹算子的半通约子方面取得了进展。我们概括了 Bauer 等人（J Funct Anal 268:3017, 2015）和 Qin（Bull Sci Math 179:103156, 2022）的结果。对于某些符号空间，我们得到两个托普利兹算子只能在三元情况下半相交，这与经典福克空间的已知情况不同。作为应用，我们考虑了 Ma 等人（J Funct Anal 277:2644-2663, 2019）中对 Fock 空间证明为假的猜想。本文的主要结果表明，福克空间和福克-索博廖夫空间的几何图形存在根本区别。

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Semi-commutants of Toeplitz Operators on Fock–Sobolev Space of Nonnegative Orders

We make a progress towards describing the semi-commutants of Toeplitz operators on the Fock–Sobolev space of nonnegative orders. We generalize the results in Bauer et al. (J Funct Anal 268:3017, 2015) and Qin (Bull Sci Math 179:103156, 2022). For the certain symbol spaces, we obtain two Toeplitz operators can semi-commute only in the trivial case, which is different from what is known for the classical Fock space. As an application, we consider the conjecture which was shown to be false for the Fock space in Ma et al. (J Funct Anal 277:2644–2663, 2019). The main result of this paper says that there is a fundamental difference between the geometries of the Fock and Fock–Sobolev space.

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来源期刊

Complex Analysis and Operator Theory 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

107

审稿时长

3 months

期刊介绍： Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.

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