Search for dissertations about: "analytic functions"

Showing result 1 - 5 of 74 swedish dissertations containing the words analytic functions.

2. 1. Invariant Subspaces in Spaces of Analytic Functions

   Author : Ali Abkar; Matematik (naturvetenskapliga fakulteten); []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; functional analysis; Series; Fourier analysis; weighted Bergman space.; super-biharmonic function; quasi-Banach space of analytic functions; index; multiplier module homomorphism; multiplier; Banach space of analytic functions; hyperinvariant subspace; Serier; fourieranalys; funktionsanalys;

   Abstract : Let D be a finitely connected bounded domain with smooth boundary in the complex plane. We first study Banach spaces of analytic functions on D . The main result is a theorem which converts the study of hyperinvariant subspaces on multiply connected domains into the study of hyperinvariant subspaces on domains with fewer holes. READ MORE

4. 2. Residue currents on analytic spaces

   Author : Richard Lärkäng; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; analytic spaces; weakly holomorphic functions; residue currents; Coleff-Herrera products; the duality theorem; weakly holomorphic functions;

   Abstract : This thesis concerns residue currents on analytic spaces. In the first paper, we construct Coleff-Herrera products and Bochner-Martinelli type currents associated with a weakly holomorphic mapping, and show that these currents satisfy well-known properties from the strongly holomorphic case. READ MORE

5. 3. A Study of Smooth Functions and Differential Equations on Fractals

   Author : Anders Pelander; Anders Öberg; Svante Janson; Alexander Teplyaev; Tom Lindström; Uppsala universitet; []
   Keywords : Mathematical analysis; Analysis on fractals; p.c.f. fractals; Sierpinski gasket; Laplacian; differential equations on fractals; infinite dimensional i.f.s.; invariant measure; harmonic functions; smooth functions; derivatives; products of random matrices; Matematisk analys;

   Abstract : In 1989 Jun Kigami made an analytic construction of a Laplacian on the Sierpiński gasket, a construction that he extended to post critically finite fractals. Since then, this field has evolved into a proper theory of analysis on fractals. The new results obtained in this thesis are all in the setting of Kigami's theory. READ MORE

6. 4. Algebras of bounded holomorphic functions

   Author : Anders Fällström; Umeå universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; holomorphic function; bounded holomorphic function; domain of holomorphy; envelope of holomorphy; Gleason’s problem; convex set; uniform algebra; spectrum; fibers; generalized Shilov boundary; analytic structure; plurisubharmonic function;

   Abstract : Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. READ MORE

7. 5. Amoebas, Discriminants, and Hypergeometric Functions

   Author : Lisa Nilsson; Mikael Passare; Maurice Rojas; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; amoeba; coamoeba; discriminant; hypergeometric functions; Mellin transform; Algebra; geometry and mathematical analysis; Algebra; geometri och analys; Mathematics; matematik;

   Abstract : This thesis consists of six chapters. In Chapter 1 we give some historical background to the topic of the thesis together with the fundamental definitions and results that the thesis is based on. In Chapter 2 we study Mellin transforms of rational functions and investigate their analytic continuations. READ MORE