If D is a bounded open subset of C", the set H = {ƒ: D —> C| ƒ is holomorphic and SD\f\ 2 < +°°} is a separable infinite-dimensional Hubert space relative to the inner product <ƒ, g) = fDfg. The completeness of H can be seen from Cauchy integral estimates. Similar estimates show that for any p E D the functional ƒ H* ƒ(/?),ƒ£ H, is continuous. Thus there is a unique element KD(z, p) E f/ (as a ...

Given a sequence of positive Hermitian holomorphic line bundles (Lp,hp) on Kähler manifold X, we establish the asymptotic expansion Bergman kernel space global sections Lp, under natural convergence assumption curvatures c1(Lp,hp). We then apply this to study distribution common zeros random sequences m-tuples Lp as p→+∞.

We characterize the space of restrictions real rational functions to certain algebraic Jordan curves in plane via Dirichlet-to-Neumann map associated domain complex bounded by curve and its Bergman kernel. The characterization leads a partial fractions-like decomposition for such new ways describe curves. multiply connected case is also explored.

We study diagonal estimates for the Bergman kernels of certain model domains in C near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as we...

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

Two Kahler manifolds are called relatives if they admit a common submanifold with the same induced metrics. In this paper, we show that Hartogs domain over an irreducible bounded symmetric equipped Bergman metric is not relative to complex Euclidean space. This generalizes results in [5, 4] and novelty here kernel of necessarily Nash algebraic.

We introduce the notion of an isotropic quantum state associated with a Bohr–Sommerfeld manifold in context Berezin–Toeplitz quantization general prequantized symplectic manifolds, and we study its semiclassical properties using off-diagonal expansion Bergman kernel. then show how these results extend to case noncompact orbifolds give application relative Poincaré series theory automorphic forms.

We extend the direct approach to semiclassical Bergman kernel asymptotics, developed recently in Deleporte et al. (Ann Fac Sci Toulouse Math, 2020) for real analytic exponential weights, smooth case. Similar (2020), our avoids use of Kuranishi trick and it allows us construct amplitude asymptotic projection by means an inversion explicit Fourier integral operator.

Scattering parameter expressions are developed for the principal mode of a coaxial air line. The model allows for skin-effect loss and dimensional variations in the inner and outer conductors. Small deviations from conductor circular cross sections are conformally mapped by the Bergman kernel technique. Numerical results are illustrated for a 7 mm air line. An error analysis reveals that the ac...

Let il be a bounded pseudoconvex domain in C" with smooth denning function r and let zo 6 bCl be a point of finite type. We also assume that the Levi form ddr(z) of bil has (n — 2)-positive eigenvalues at z0 . Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense.