where dist denotes the Euclidean distance. Note that for Lipα(D) and A∞ the zero sequences Z are characterized by (1) and (2), with S replaced by Z. 3. The Blaschke sets S for the class D of analytic functions with finite Dirichlet integral are characterized by (2) (see [B]). Note that D-zero sequences cannot be described this way because there are f ∈ D whose zeros come arbitrarily close to ev...

Let Ω be a bounded pseudoconvex domain in C N , φ, ψ two positive functions on Ω such that − logψ,− log φ are plurisubharmonic, z ∈ Ω a point at which − log φ is smooth and strictly plurisubharmonic, and M a nonnegative integer. We show that as k → ∞, the Bergman kernels with respect to the weights φkψM have an asymptotic expansion KφkψM (x, y) = kN πNφ(x, y)kψ(x, y)M ∞ ∑ j=0 bj(x, y) k −j , b0...

In the present paper, the author shows that if a homogeneous submodule M of the Bergman module La(Bd) satisfies PM − ∑ i MziPMM ∗ zi ≤ c N + 1 PM for some number c > 0, then there is a sequence {fj} of multipliers and a positive number c′ such that c′PM ≤ ∑ j Mfj M ∗ fj ≤ PM, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules a...

The Bergman cyclization of the natural enediyne dynemicin A in its triggered form (2) bound to the minor groove of DNA is compared with the corresponding reaction of its open isomer (4) utilizing QM/MM methodology. The two isomers are typical representatives of 10-membered cyclic (2) and acyclic (4) enediynes, which possess significantly different barriers for the Bergman reaction in the gas ph...

In this paper, we investigate singular integral operators induced by the Bergman kernel and Szegö on irreducible bounded symmetric domain in its standard Harish-Chandra realization. We completely characterize when Bergman-type Szegö-type belong to Schatten class operator ideals several analytic numerical invariants of domain. These results not only generalize a recent result Hilbert unit ball d...

We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated to such a line bundle.

Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operator...

In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite dimensional and it is dual to the the Bergman space on the pseudoconvex domain Ω−. The duality is further identified e...

natural light is one kind of light which its main resources are sun and starts. philosophers and researchers believe that spiritual and holy light not only includes material and quantified aspect, but also because of its non-physical properties always treats as a spiritual connector between god and man. light is the main part of existing which not only contacts to the surface of objects, but it...