This article contains a detailed study in the case of a toric variety of the geodesic rays φt defined by Phong-Sturm corresponding to test configurations T in the sense of Donaldson. We show that the ‘Bergman approximations’ φk(t, z) of Phong-Sturm converge in C to the geodesic ray φt, and that the geodesic ray itself is C 1,1 and no better. In particular, the Kähler metrics ωt = ω0 + i∂∂̄φt ass...

D |f(z)|dμ(z) )︀1/p < ∞ and by La(D, dμ) (or La(D) for short) the subspace of the space L(D) comprising the functions that are analytic on D. If p = 2, La(D) is a Hilbert subspace of L2(D) and it is called Bergman space. Let P denote the orthogonal projector of L2(D) on La(D) (Bergman projection). Let {δn}n=0 be defined by δn = (︀ 2π ∫︀ 1 0 r 2n+1w(r) dr )︀1/2 . Then, the sequence of functions ...

The expansion of reproducing kernels of Bergman spaces of holomorphic functions on a domain D in Cn is of considerable interests. If the domain admits an action of a compact group K, then naturally one would like to decompose the space of polynomials into irreducible subspaces of K and expand the reproducing kernels in terms of the reproducing kernels of the finite dimensional subspaces. In [5]...

A series of [b]-fused 6,7-diethynylquinoxaline derivatives have been synthesized through an imine condensation strategy to examine the effect of extended benzannelation on the thermal reactivity of enediynes. Absorption and emission spectra of the highly conjugated quinoxalenediynes were red-shifted approximately 100-200 nm relative to those of 1,2-diethynylbenzene. Strong exotherms indicative ...

COMPACT COMPOSITION OPERATORS ON THE HARDY AND BERGMAN SPACES

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...