We present several embedding results for 3-graded Lie algebras and KKT algebras that are generated by two homogeneous elements of degrees 1 and −1. We also propose the canonical kernel function for a “universal Bergman kernel” which extends the usual Bergman kernel on a bounded symmetric domain to a group-valued function or, in terms of formal series, to an element in the formal completion of t...

We compute the explicit formula of the Bergman kernel for a nonhomogeneous domain {(z1, z2) ∈ C2 : |z1|1 + |z2|2 < 1} for any positive integers q1 and q2. We also prove that among the domains Dp := {(z1, z2) ∈ C2 : |z1|1 + |z2|2 < 1} in C2 with p = (p1, p2) ∈ N2, the Bergman kernel is represented in terms of closed forms if and only if p = (p1, 1), (1, p2), or p = (2, 2).

Cory Hawkins,* D. Scott Wills, Odile Liboiron-Ladouceur, and Keren Bergman School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, Georgia 30332-0250, USA Department of Electrical Engineering, Columbia University in the City of New York, 500 West 120th Street, New York, New York 10027, USA E-mail: [email protected] E-mail: ol2007@...

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...

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 ...

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]...

COMPACT COMPOSITION OPERATORS ON THE HARDY AND BERGMAN SPACES

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...

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...