The orthogonal projection from a Sobolev space WS(Q) onto the subspace of holomorphic functions is studied. This analogue of the Bergman projection is shown to satisfy regularity estimates in higher Sobolev norms when ß is a smooth bounded strictly pseudoconvex domain in C". The Bergman projection P0: L2(ü) -» L2(S2) n {holomorphic functions}, where S2 c C" is a smooth bounded domain, has prove...

Bergman complexes are polyhedral complexes associated to matroids. Faces of these complexes are certain matroids, called matroid types, too. In order to understand the structure of these faces we decompose matroid types into direct summands. Ardila/Klivans proved that the Bergman Complex of a matroid can be subdivided into the order complex of the proper part of its lattice of flats. Beyond tha...

We study the Bergman kernel and projection on the worm domains Dβ = { ζ ∈ C : Re ( ζ1e −i log |ζ2| 2) > 0, ∣∣ log |ζ2| ∣∣ < β − π 2 } and D β = { z ∈ C : ∣Im z1 − log |z2| ∣∣ < π 2 , | log |z2| | < β − π 2 } for β > π. These two domains are biholomorphically equivalent via the mapping D β ∋ (z1, z2) 7→ (e z1 , z2) ∋ Dβ . We calculate the kernels explicitly, up to an error term that can be contr...

We consider the so-called Berezin ?-sequence, where ? is an operator valued inner function, for operators on vector Hardy space H2E (D), and study invertibility of some model K? = ?H2E via ?-sequence. By applying symbols technique Toeplitz corona problem in Bergman L2a(D) studied. Moreover, C-invertibility C-unitarity are also defined

In this note, we point out that a large family of n × n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered usi...

Abstract We study the Bergman metric of a finite ball quotient $\mathbb{B}^n/\Gamma $, where $n \geq 2$ and $\Gamma \subseteq{\operatorname{Aut}}({\mathbb{B}}^n)$ is finite, fixed point free, abelian group. prove that this Kähler–Einstein if only $ trivial, is, when unit ${\mathbb{B}}^n$ itself. As consequence, we characterize among normal Stein spaces with isolated singularities fundamental gr...

Scattering parameter expressions are developed for the principal mode of a coaxial air line. The model allows for skin-effect loss and dimensional variations in the inner and outer conductors. Small deviations from conductor circular cross sections are conformally mapped by the Bergman kernel technique. Numerical results are illustrated for a 7 mm air line. An error analysis reveals that the ac...

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_...