The effective resistivity and conductivity of two media that meet at a randomly rough interface are computed in the quasistatic limit. The results are presented in the spectral density representations of the Bergman-Milton formulation for the properties of two-component composite materials. The spectral densities are extracted from computer simulations of resistor networks in which the random i...

We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, we study the asymptotic expansion of the G-invariant Bergman kernel of the spinc Dirac operator associated with high tensor powers of a positive line bundle on a symplectic manifold...

In this article, we construct the canonical semipositive current or the canonical measure (= the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical system of Bergman kernels. This current is considered to be a generalization of a Kähler-Einstein metric and coincides the one considered independently by J. Song ...

Acclaimed as one of the great filmmakers of the 20th century, Ingmar Bergman is for many an arch-modernist, whose work is characterized by a high degree of self-conscious artistry and by dark, even nihilistic themes. Film critics increasingly identify him as a kind of philosopher of the human condition, especially of the dislocations and misery of the modern human condition. However, Bergman’s ...

We establish universality type limits for Bergman orthogonal polynomials on simply connected regions in the complex plane with smooth boundary. Keywords: Universality Limits, Bergman Polynomials AMS Classi…cation: 41A55, 65D30, 65B99, 42C99 Research supported by NSF grant DMS0700427 and US-Israel BSF grant 2004353 1. Introduction and Results Let G be a bounded simply connected domain in the com...

1.1. Definitions Throughout this paper, λ denotes the Lebesgue measure on C and ωo = dd|z| the Euclidean Kähler form in C, where d = √ −1 4 (∂̄ − ∂). Let φ ∈ C (C) be a function, μ a measure in C, and p ∈ [1,∞). One can define the spaces Lp(e−pφdμ) and F (μ, φ) := Lp(e−pφdμ) ∩ O(C). If the measure μ is Lebesgue measure, we simply write F (λ, φ) =: F (φ). Similarly one can define L∞(e−φ, μ) = {f ...

In this paper, we characterize the hyponormal dual Toeplitz operators with special symbols on orthogonal complement of pluriharmonic Bergman space unit ball. Also completely for (semi)commuting operators.

We consider the problem of L1 (un)boundedness for a wide class orthogonal projections, including Bergman projections on domains in complex manifolds and Szegö abstract CR manifolds.

We prove two sharp estimates for the subspace of a standard weighted Bergman space that consists functions vanishing at given point (with prescribed multiplicity).

Recently, Douglas and Wang proved that for each polynomial q, the submodule [q] of the Bergman module generated by q is essentially normal [9]. Using improved techniques, we show that the Hardy-space analogue of this result holds, and more.