Berezin regularity of domains in $\mathbb {C}^n$ and the essential norms of Toeplitz operators
Copyright policy )Berezin regularity of domains in $\mathbb {C}^n$ and the essential norms of Toeplitz operators
For the open unit disc $\mathbb{D}$ in the complex plane, it is well known that if $ϕ\in C(\overline{\mathbb{D}})$ then its Berezin transform $\widetildeϕ$ also belongs to $C(\overline{\mathbb{D}})$. We say that $\mathbb{D}$ is BC-regular. In this paper we study BC-regularity of some pseudoconvex domains in $\mathbb{C}^n$ and show that the boundary geometry plays an important role. We also establish a relationship between the essential norm of an operator in a natural Toeplitz subalgebra and its Berezin transform.
Fixed few typos. Minor changes. To appear in Trans. Amer. Math. Soc
- University System of Ohio United States
- University of Toledo United States
convex domain, Mathematics - Complex Variables, Bergman kernel, \( \overline{\partial}\)-Neumann operator, pseudoconvex domain, Functional Analysis (math.FA), Berezin transform, Mathematics - Functional Analysis, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators
convex domain, Mathematics - Complex Variables, Bergman kernel, \( \overline{\partial}\)-Neumann operator, pseudoconvex domain, Functional Analysis (math.FA), Berezin transform, Mathematics - Functional Analysis, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!