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.

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...

We consider the problem of …nding the best analytic approximation in Smirnov and Bergman norm to general monomials of the type znzm. We show that in the case of approximation to z in the annulus (and the disk) the best approximation is the same for all values of p. Moreover, the best approximations to z in Smirnov and Bergman spaces characterize disks and annuli.

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

We prove that the lattice EqΩ of all equivalence relations on an infinite set Ω contains, as a 0, 1-sublattice, the 0-coproduct of two copies of itself, thus answering a question by G.M. Bergman. Hence, by using methods initiated by de Bruijn and further developed by Bergman, we obtain that EqΩ also contains, as a sublattice, the coproduct of 2 Ω copies of itself.

Philip J. Bergman*, Jedd D. Wolchok 1 Bright Heart Veterinary Centers Ludwig Center for Cancer Immunotherapy, Memorial Sloan-Kettering Cancer Center __________________________________________________________________________________ *Correspondence: Philip J. Bergman DVM, MS, PhD, Diplomate ACVIM-Oncology, Chief Medical Officer, Bright Heart Veterinary Centers, 80 Business Park Drive, Suite 110,...