(Strictly speaking, one should put ( —1)"2/2 in front of £)'> but this is not essential in the following discussion.) Suppose F is ample in the following sense: (A.l). For every z in M, there exists an/ in F which does not vanish at 2. (A.2). For every holomorphic vector Z at z, there exists an/ in F such that / vanishes at z and Z(f *) ^0, where /=/ * dz1 A ■ ■ • Adzn with respect to a local c...

In this paper we study the complete invariant metrics on CartanHartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, w...

In this paper, we characterize the boundedness and compactness of weighted composition operators ψCφf = ψfoφ acting between Bergman-type spaces.

We define positive Toeplitz operators between harmonic Bergman–Besov spaces $$b^p_\alpha $$ on the unit ball of $${\mathbb {R}}^n$$ for full ranges parameters $$0<p<\infty , $$\alpha \in {\mathbb {R}}$$ . give characterizations bounded and compact taking one space into another in terms Carleson vanishing measures. also a operator $$b^{2}_{\alpha }$$ to be Schatten class $$S_{p}$$ averaging func...

We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.

The minimum variance performance measure is applied to two diabetic patient models under simulated fault scenarios. The Bergman Model and the Automated Insulin Dosage Advisor (AIDA), are controlled in the Internal Model Control (IMC) framework to achieve adequate blood glucose levels. The focus of this paper is to reect the importance and feasibility of implementing a detection and diagnosis to...

The Szego projection preserves global smoothness in weakly pseudoconvex domains that are regular in the sense of Diederich, Fornaess, and Catlin. It preserves local smoothness near boundary points of finite type. The Bergman projection, being linked to the 3 problem, plays an important role in several complex variables, as demonstrated by recent applications to the boundary behavior of holomorp...

In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one. We prove several sufficient conditions and necessary and sufficient conditions for a weight to be...

We apply Forelli-Rudin construction and Nakazawa’s hodograph transformation to prove a graph theoretic closed formula for invariant theoretic coefficients in the asymptotic expansion of the Szegö kernel on strictly pseudoconvex complete Reinhardt domains. The formula provides a structural analogy between the asymptotic expansion of the Bergman and Szegö kernels. It can be used to effectively co...