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Deformation theory for algebras of analytic functions. (English) Zbl 0701.46042
Deformation theory of algebras and structures and applications, Nato Adv. Study Inst., Castelvecchio-Pascoli/Italy 1986, Nato ASI Ser., Ser. C 247, 501-535 (1988).
Summary: [For the entire collection see Zbl 0654.00006.]
This is a very informal introduction to the theory of deformation of Banach algebras of analytic functions on finite bordered (possibly singular) Riemann surfaces. The main focus is the interaction between the deformation theory of Banach algebras and the deformation theory associated with the (singular and non-singular) Riemann surfaces. My main goal is to indicate how the sets of ideas fit together. Some discussion will be made of proof techniques, but no proofs will be given. The section of references at the end contains brief comments on the location of the proofs.
##### MSC:
 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
Zbl 0654.00006