Bergman kernel function and canonical slit-mapping.
نویسندگان
چکیده
منابع مشابه
The Bergman Kernel Function
In this note, we point out that a large family of n × n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. We show that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can be answered usi...
متن کاملCanonical coordinates and Bergman metrics
In this paper we will discuss local coordinates canonically corresponding to a Kähler metric. We will also discuss the C ∞ convergence of Bergman metrics following Tian's result on C 2 convergence of Bergman metrics. At the end we present an interesting characterization of ample line bundle that could be useful in arithmetic geometry.
متن کاملThe Bergman Kernel Function and Proper Holomorphic Mappings
It is proved that a proper holomorphic mapping / between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, /~'(0) = {0}, then / is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.
متن کاملSome Inequalities Relating to Conformal Mapping upon Canonical Slit-domains
(1) f = se(z) = z + — + • • • z and which maps D conformally and bi-uniformly upon a domain De of the f-plane bounded by n rectilinear slits each of which makes the angle 0 with the positive direction of the real axis. The domain De is itself also uniquely determined for each value of 0. In the present paper we shall derive two inequalities involving the coefficient a$ appearing in (1) and the ...
متن کاملThe Bergman Kernel Function of Some Reinhardt Domains
The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z, z̄). Let D be the Reinhardt domain D = { z ∈ C | ‖z‖α = n ∑
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1953
ISSN: 2156-2261
DOI: 10.1215/kjm/1250777509