Abstract In this paper we introduce a new distance by means of the so-called Szegő kernel and examine some basic properties its relationship with Skwarczyński distance. We also between distance, Bergman

In this paper, we study the Bergman kernel Bφ(x,y) of generalized Bargmann-Fock spaces in setting Clifford algebra. The versions L2-estimate method and weighted subharmonic inequality for algebra are established. Consequently show existence then give some estimates on- off- diagonal. As a by-product, also obtain an upper estimate harmonic kernel.

If A is a unital weak-∗ closed subalgebra of a multiplier algebra on a reproducing kernel Hilbert space which has property A1(1), then the cyclic invariant subspaces provide an Nevanlinna-Pick (NP) family of kernels. This yields an NP interpolation theorem for a wide class of operator algebras. In particular, it applies to many kernel spaces over the unit disk including the Bergman space. We al...

In this paper, a comparison between the Bergman kernel form and pushforward measure of Masur-Veech on Teichmüller space genus g ≥ 2 <mml:annotation encoding...

Fefferman [22] initiated a program of expressing the asymptotic expansion of the boundary singularity of the Bergman kernel for strictly pseudoconvex domains explicitly in terms of boundary invariants. Hirachi, Komatsu and Nakazawa [30] carried out computations of the first few terms of Fefferman’s asymptotic expansion building partly on Graham’s work on CR invariants and Nakazawa’s work on the...

A property of the Bergman projection associated to a bounded circular domain containing the origin in C^ is proved: Functions which extend to be holomorphic in large neighborhoods of the origin are characterized as Bergman projections of smooth functions with small support near the origin. For certain circular domains D, it is also shown that functions which extend holomorphically to a neighbor...