Sökning: "holomorphic functions"
Visar resultat 1 - 5 av 32 avhandlingar innehållade orden holomorphic functions.
1. Algebras of bounded holomorphic functions
Sammanfattning : 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. LÄS MER
2. Holomorphic functions on polydiscs and measures on the distinguished boundary
Sammanfattning : This thesis consists of four papers, treating holomorphic functions defined on polydiscs, operators acting on spaces of such functions, and related measures on the n-torus. In paper I we study containment of rational inner functions, or RIFs for short, in Dirichlet type spaces on the unit polydisc D^n. LÄS MER
3. Ideals and boundaries in Algebras of Holomorphic functions
Sammanfattning : We investigate the spectrum of certain Banach algebras. Properties like generators of maximal ideals and generalized Shilov boundaries are studied. LÄS MER
4. Envelopes of holomorphy for bounded holomorphic functions
Sammanfattning : Some problems concerning holomorphic continuation of the class of bounded holomorphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Gleason’s Problem for H°°(Ω) cannot be solved. LÄS MER
5. Integral representations of Herglotz-Nevanlinna functions
Sammanfattning : In this thesis, we study integral representations of Herglotz-Nevanlinna functions, that is to say holomorphic functions defined on a product of several copies of the complex upper half-plane having non-negative imaginary part. The manuscript is divided into three parts, beginning with a general introduction followed by two papers. LÄS MER