Simplicity of the Bergman, Szego and Poisson kernel functions
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 کاملOn the Asymptotic Expansion of Bergman Kernel
We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.
متن کاملThe Stability of the Bergman Kernel and the Geometry of the Bergman Metric
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 ...
متن کاملSubharmonicity Properties of the Bergman Kernel and Some Other Functions Associated to Pseudoconvex Domains
Let D be a pseudoconvex domain in Ckt × C n z and let φ be a plurisubharmonic function in D. For each t we consider the ndimensional slice of D, Dt = {z; (t, z) ∈ D}, let φ be the restriction of φ to Dt and denote by Kt(z, ζ) the Bergman kernel of Dt with the weight function φ. Generalizing a recent result of Maitani and Yamaguchi (corresponding to n = 1 and φ = 0) we prove that logKt(z, z) is ...
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: Mathematical Research Letters
سال: 1995
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1995.v2.n3.a4