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Invariant spaces and traces of holomorphic functions on the skeletons of classical domains. (English. Russian original) Zbl 0629.32012

Sib. Math. J. 25, 167-175 (1984); translation from Sib. Mat. Zh. 25, No. 2(144), 3-12 (1984).
In the paper D denotes a classical domain in the space of several complex variables, i.e., an irreducible symmetric domain of one of the four types, clearly specified A(D) is the algebra of the functions, continuous in the closed domain D and holomorphic in D. \(\Gamma\) is the skeleton of D i.e., the Shilov boundary of A(D). A(\(\Gamma)\) is the restriction of the algebra A(D) to \(\Gamma\) and C(\(\Gamma)\) is the space of complex- valued functions on \(\Gamma\) with uniform norm. G denotes the group of bi-holomorphic automorphism of D. The invariant subspace of the space C(\(\Gamma)\) for D is studied here, after invariant spaces are defined clearly. Some interesting results about invariant subspaces are proved.
Reviewer: M.Dutta

MSC:

32A38 Algebras of holomorphic functions of several complex variables
46J10 Banach algebras of continuous functions, function algebras
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
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References:

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