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 present a method of obtaining a lower bound estimate of the curvatures of the Bergman metric without using the regularity of the kernel function on the boundary. As an application, we prove the existence of an uniform lower bound of the bisectional curvatures of the Bergman metric of a smooth bounded pseudoconvex domain near the boundary with constant Levi rank.

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.

In this note, we explain that Ross–Thomas’ result [4, Theorem 1.7] on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result [1]. This result plays an important role in the companion paper [5] to prove an orbifold version of Donaldson theorem. In two very interesting papers [4, 5], Ross–Thomas describe a notion of ampleness for line bundles on Kähler orbifold...

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,...

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

We characterise the boundedness of a Toeplitz operator on the Bergman space with a L symbol. We also prove that the compactness of a Toeplitz operator on the Bergman space with a L symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends known results in the cases when the symbol is either a positive L function, an L∞ function or a general BMO func...