For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. In particular, the Bergman spaces of these manifolds are infinite-dimensional.

The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z, z̄). Let D be the Reinhardt domain D = { z ∈ C | ‖z‖α = n ∑

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line bundles.

We obtain a conceptually new differential geometric proof of P.F. Klembeck’s result (cf. [9]) that the holomorphic sectional curvature kg(z) of the Bergman metric of a strictly pseudoconvex domain Ω ⊂ C approaches −4/(n + 1) (the constant sectional curvature of the Bergman metric of the unit ball) as z → ∂Ω.

Thermal Bergman cyclization of Pt(II) dialkynylporphyrins reveals a marked reduction in the cyclization temperature relative to the free base and Zn(II) derivatives. In contrast, photogenerated (3)ππ* population produces no detectable Bergman photocyclization, suggesting that the photoreactivities of the related free base and Zn(II) derivatives occurs via the (1)ππ* state.

The article is based on experience of implementation of computer algebra system Bergman and on analysis of other symbolic computation systems. It is noted that many symbolic computation systems meet similar interface problems. Necessity of strict separation of calculation engine and interface shell, functions of these components, and requirements to them are motivated. The described approach wi...

Canonical divisors in Bergman spaces can be found as solutions of extremal problems. We derive a formula for certain extremal functions in the weighted Bergman spaces Aα for α > −1 and 1 ≤ p <∞. This leads to a study of the zeros of a specific family of hypergeometric functions.

We treat the complex harmonic function on the Np–ball which is defined by the Np–norm related to the Lie norm. As a subspace, we treat Hardy spaces and consider the Bergman kernel on those spaces. Then, we try to construct the Bergman kernel in a concrete form in 2–dimensional Euclidean space. Introduction. In [2], [4], [6] and [7], we studied holomorphic functions and analytic functionals on t...

Let D be a bounded domain in C". The invariant distance in D is given by I I v I \ is l \\ '/2\ l/2 Kp(z,i)K„(w,w) It is shown that one half of the length of a piecewise C1 curve y: [a, b] -* D with respect to the Bergman metric is equal to the length of y measured by pD, which implies that the associated inner distance p*D coincides (up to the factor {) with the Bergman-distance. Also it was p...