Approximate Representation of Bergman Submodules∗

Essential Normality of Polynomial-generated Submodules: Hardy Space and Beyond

Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [9]. Using improved techniques, we show that the Hardy-space analogue of this result holds, and more.

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

. FA ] 2 6 Ju l 2 00 5 A new kind of index theorem ∗

Index theory has had profound impact on many branches of mathematics. In this note we discuss the context for a new kind of index theorem. We begin, however, with some operator-theoretic results. In [11] Berger and Shaw established that finitely cyclic hyponormal operators have trace-class self-commutators. In [9], [31] Berger and Voiculescu extended this result to operators whose self-commutat...

Self-commutators of composition operators with monomial symbols on the Bergman space

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies

In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet's principles, is concurrently able to be expanded in Taylor's representation, over a particular interval of their do...