Let ⊂ R be a bounded, convex, and open set with real analytic boundary. Let T ⊂ C be the tube with base , and let B be the Bergman kernel of T . If is strongly convex, then B is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation we relate the off-diagonal points where analyticity fails to the characteristic lines. These lines are contai...

The main purpose of the following article is to give a proof of Y. Kawa-mata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an L 2 m –extension theorem of Ohsawa-Takegoshi type (which is also a new result) and a more complete version of our former results. §0 Introduction Let X be a projective manifold and let Θ be a ...

We use some results from the theory of reproducing kernel Hilbert spaces to show that reachable space heat equation for a finite rod with either one or two Dirichlet boundary controls is RKHS analytic functions on square, and we compute its as an infinite double series. also null half line data sector, whose (essentially) sum pullbacks Bergman Hardy kernels plane \(\mathbb {C}^+\).

Let Ω be a non-compact complex manifold of dimension n, ω = ∂∂Ψ a Kähler form on Ω, and Kα(x, y) the reproducing kernel for the Bergman space Aα of all analytic functions on Ω square-integrable against the measure e−αΨ|ωn|. Under the condition Kα(x, x) = λαe αΨ(x) F. A. Berezin [Math. USSR Izvestiya 8 (1974), 1109–1163] was able to establish a quantization procedure on (Ω, ω) which has recently...