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Hardy type spaces associated with compact unitary groups. (English) Zbl 1210.46029

Summary: We investigate Hilbertian Hardy type spaces of complex analytic functions of infinitely many variables, associated with compact unitary groups and the corresponding invariant Haar measures. For such analytic functions, we establish a Cauchy type integral formula and describe natural domains. Also, we show some relations between the constructed spaces of analytic functions and the symmetric Fock space.

MSC:

46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
42B30 \(H^p\)-spaces
46G20 Infinite-dimensional holomorphy
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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