Sökning: "weakly holomorphic functions"

Hittade 4 avhandlingar innehållade orden weakly holomorphic functions.

1. 1. The Maximum Principle for Cauchy-Riemann Functions and Hypocomplexity

   Författare :Abtin Daghighi; Stefan Borell; Christer Kiselman; Egmont Porten; Juergen Leiterer; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Hypocomplexity; hypoanalytic structure; CR functions; maximum principle; weak pseudoconcavity;

   Sammanfattning : This licentiate thesis contains results on the maximum principle forCauchy–Riemann functions (CR functions) on weakly 1-concave CRmanifolds and hypocomplexity of locally integrable structures. Themaximum principle does not hold true in general for smooth CR functions,and basic counterexamples can be constructed in the presenceof strictly pseudoconvex points. LÄS MER

3. 2. Residue currents on analytic spaces

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

   Sammanfattning : 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. LÄS MER

4. 3. Residue currents on singular varieties

   Författare :Richard Lärkäng; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; weakly holomorphic functions; duality theorem; Coleff-Herrera products; Bochner-Martinelli currents; residue currents; singular varieties; analytic spaces; local analytic geometry; residue currents;

   Sammanfattning : This thesis concerns various aspects of the theory of residue currents. Particularly, we study residue currents on singular varieties and duality theorems for such currents. On a singular variety, there are various notions of holomorphic functions. LÄS MER

5. 4. Regularity and uniqueness-related properties of solutions with respect to locally integrable structures

   Författare :Abtin Daghighi; Egmont Porten; Christer Kiselman; Stefan Borell; Jürgen Leiterer; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Maximum principle; hypocomplexity; locally integrable structure; hypoanalytic structure; weak pseudoconcavity; uniqueness; CR functions;

   Sammanfattning : We prove that a smooth generic embedded CR submanifold of C^n obeys the maximum principle for continuous CR functions if and only if it is weakly 1-concave. The proof of the maximum principle in the original manuscript has later been generalized to embedded weakly q-concave CR submanifolds of certain complex manifolds. LÄS MER