Search for dissertations about: "weighted Bergman kernel"

Found 5 swedish dissertations containing the words weighted Bergman kernel.

2. 1. Weighted Bergman kernels and biharmonic Green functions

   Author : Stefan Jakobsson; Matematikcentrum; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; singularity resolution of Bergman kernels; Hadamard s variational formula; weighted Bergman kernel; weighted biharmonic Green function; Friedrichs operator; Plant biochemistry; Växtbiokemi;

   Abstract : The main theme of this thesis is the connection between weighted biharmonic Green functions and weighted Bergman kernels. In the first paper, which is a joint work with H. Hedenmalm and S. Shimorin, we prove that weighted biharmonic Green functions are positive for weights which satisfy a mean-value condition and whose logarithms are subharmonic. READ MORE

4. 2. Reproducing kernels and potential theory for the Bergman spaces

   Author : Yolanda Perdomo Gallipoli; Matematikcentrum; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; weighted biharmonic Green function Gaussian curvature; Naturvetenskap; harmonic compensator; Natural science; weighted super-biharmonic function; potential metric; mean value property; weighted Bergman kernel;

   Abstract : The role of weighted biharmonic Green functions in weighted Bergman spaces was first studied in the beginning of the 50's by Paul Garabedian. In 1951 he showed that they are closely related to reproducing kernel functions of weighted Bergman spaces. READ MORE

5. 3. Conformal Maps, Bergman Spaces, and Random Growth Models

   Author : Alan Sola; Haakan Hedenmalm; Robert Berman; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Conformal maps; Bergman kernels; planar growth models; MATHEMATICS; MATEMATIK;

   Abstract : This thesis consists of an introduction and five research papers on topics related to conformal mapping, the Loewner equation and its applications, and Bergman-type spaces of holomorphic functions. The first two papers are devoted to the study of integral means of derivatives of conformal mappings. READ MORE

6. 4. Bergman space methods and integral means spectra of univalent functions

   Author : Alan Sola; Håkan Hedenmalm; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Univalent functions; integral means spectra; Bergman spaces; Algebra; geometry and mathematical analysis; Algebra; geometri och analys;

   Abstract : We study universal integral means spectra of certain classes of univalent functions defined on subsets of the complex plane. After reformulating the definition of the integral means spectrum of a univalent function in terms of membership in weighted Bergman spaces, we describe the Hilbert space techniques that can be used to estimate universal means spectra from above. READ MORE

7. 5. Hankel operators and Plancherel formula

   Author : Genkai Zhang; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES;

   Abstract : We consider the natural unitary action of the group SU(d, 1) on the Hilbert space L2(B,d/j,\), where B is the unit ball of C , dfi\ is the measure K(z, z)~~*+ï dm(z), and K(z, z) the reproducing kernel of the Bergman space on B. For A >—1 and not an integer, a Plancherel formula is proved for this action and, in particular, an explicit formula for the correponding Plancherel measure is found. READ MORE