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Ideals and boundari...
Ideals and boundaries in Algebras of Holomorphic functions
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- Carlsson, Linus, 1972- (författare)
- Mälardalens högskola,Umeå universitet,Institutionen för matematik och matematisk statistik,Akademin för utbildning, kultur och kommunikation
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- Fällström, Anders, Docent (preses)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Wiegerinck, Jan, Professor (opponent)
- Korteweg-de Vries Institute for Mathematics
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(creator_code:org_t)
- ISBN 9172640111
- Umeå : Umeå universitet, 2006
- Engelska 97 s.
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Serie: Doctoral thesis / Umeå University, Department of Mathematics, 1102-8300 ; 33
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Abstract
Ämnesord
Stäng
- We investigate the spectrum of certain Banach algebras. Properties like generators of maximal ideals and generalized Shilov boundaries are studied. In particular we show that if the ∂-equation has solutions in the algebra of bounded functions or continuous functions up to the boundary of a domain D ⊂⊂ Cn then every maximal ideal over D is generated by the coordinate functions. This implies that the fibres over D in the spectrum are trivial and that the projection on Cn of the n − 1 order generalized Shilov boundary is contained in the boundary of D.For a domain D ⊂⊂ Cn where the boundary of the Nebenhülle coincide with the smooth strictly pseudoconvex boundary points of D we show that there always exist points p ∈ D such that D has the Gleason property at p.If the boundary of an open set U is smooth we show that there exist points in U such that the maximal ideals over those points are generated by the coordinate functions.An example is given of a Riemann domain, Ω, spread over Cn where the fibers over a point p ∈ Ω consist of m > n elements but the maximal ideal over p is generated by n functions.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- maximal ideal space
- the Gleason problem
- generalized Shilov boundaries
- Nebenhülle
- the Koszul complex
- Banach algebras of holomorphic functions
- MATHEMATICS
- MATEMATIK
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