اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدZero products of Toeplitz operators on Reinhardt domains
70
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $Omega$ be a bounded Reinhardt domain in $mathbb{C}^n$ and $phi_1,ldots,phi_m$ be finite sums of bounded quasi-homogeneous functions. We show that if the product of Toeplitz operators $T_{phi_m}cdots T_{phi_1}=0$ on the Bergman space on $Omega$, then $phi_j=0$ for some $j$.
قيم البحث
اقرأ أيضاً
We prove some characterizations of Schatten class Toeplitz operators on Bergman spaces of tube domains over symmetric cones for small exponents.
Toeplitz operators are met in different fields of mathematics such as stochastic processes, signal theory, completeness problems, operator theory, etc. In applications, spectral and mapping properties are of particular interest. In this survey we wil
l focus on kernels of Toeplitz operators. This raises two questions. First, how can one decide whether such a kernel is non trivial? We will discuss in some details the results starting with Makarov and Poltoratski in 2005 and their succeeding authors concerning this topic. In connection with these results we will also mention some intimately related applications to completeness problems, spectral gap problems and P{o}lya sequences. Second, if the kernel is non-trivial, what can be said about the structure of the kernel, and what kind of information on the Toeplitz operator can be deduced from its kernel? In this connection we will review a certain number of results starting with work by Hayashi, Hitt and Sarason in the late 80s on the extremal function.
In this paper, we investigate the boundedness of Toeplitz product $T_{f}T_{g}$ and Hankel product $H_{f}^{*} H_{g}$ on Fock-Sobolev space for two polynomials $f$ and $g$ in $z,overline{z}inmathbb{C}^{n}$. As a result, the boundedness of Toeplitz oper
ator $T_{f}$ and Hankel operator $H_{f}$ with the polynomial symbol $f$ in $z,overline{z}inmathbb{C}^{n}$ is characterized.
The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in $mathbb C^2$. Our class is self-dual; it contains some domains with less than $C^2$-smooth boundary and also some domains with smooth boundary a
nd degenerate Levi form. $L^2$-regularity is proved, and essential spectra are computed with respect to a family of boundary measures which includes surface measure. A duality principle is established providing explicit unitary equivalence between operators on domains in our class and operators on the corresponding polar domains. Many of these results are new even for the classical case of smoothly bounded strongly convex Reinhardt domains.
In this paper we discuss the multipliers between range spaces of co-analytic Toeplitz operators.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
