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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:
46E50Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
42B30H p -spaces (Fourier analysis)
46G20Infinite dimensional holomorphy
46J15Banach algebras of differentiable or analytic functions, H p -spaces
References:
[1]Aron, R. M.; Cole, B. J.; Gamelin, T. W.: Spectra of algebras of analytic functions on a Banach space, J. reine angew. Math. 415, 51-93 (1991) · Zbl 0717.46031 · doi:crelle:GDZPPN002208377
[2]Aron, R. M.; Cole, B. J.; Gamelin, T. W.: Weak-star continuous analytic funtions, Canad. J. Math. 47, 673-683 (1995) · Zbl 0829.46034 · doi:10.4153/CJM-1995-035-1
[3]Carne, T. K.; Cole, B.; Gamelin, T. W.: A uniform algebra of analytic functions on a Banach space, Trans. amer. Math. soc. 314, 639-659 (1989) · Zbl 0704.46033 · doi:10.2307/2001402
[4]Cole, B.; Gamelin, T. W.: Representing measures and Hardy spaces for the infinite polydisk algebra, Proc. lond. Math. soc. 53, 112-142 (1986) · Zbl 0624.46032 · doi:10.1112/plms/s3-53.1.112
[5]Davie, A. M.; Gamelin, T. W.: A theorem on polynomial-star approximation, Proc. amer. Math. soc. 106, 351-356 (1989) · Zbl 0683.46037 · doi:10.2307/2048812
[6]Gamelin, T. W.: Analytic functions on Banach spaces, NATO adv. Sci. inst. Ser. C math. Phys. sci. 439 (1994) · Zbl 0803.46049
[7]Lopushansky, O. V.; Zagorodnyuk, A. V.: Representing measures and infinite-dimensional holomorphy, J. math. Anal. appl. 333, No. 2, 614-625 (2007) · Zbl 1131.46033 · doi:10.1016/j.jmaa.2006.09.035
[8]Rudin, W.: Function theory in the unit ball of cn, (1980)
[9]Hewitt, E.; Ross, K. A.: Abstract harmonic analysis, Abstract harmonic analysis 2 (1970) · Zbl 0213.40103
[10]Berezanski, Yu.M.; Kondratiev, Yu.G.: Spectral methods in infinite-dimensional analysis, (1995)
[11]Dineen, S.: Complex analysis on infinite dimensional spaces, Monographs in mathematics (1999)
[12]Gamelin, T. W.: Uniform algebras, (1984)
[13]K.H. Neeb, B. Ørted, Hardy spaces in an infinite dimensional setting, in: Proceedings of II International Workshop Lie Theory and its Application in Physics, vol. 6, 1998, pp. 3–27.
[14]Lopushansky, O. V.; Zagorodnyuk, A. V.: Hilbert spaces of analytic functions of infinitely many variables, Ann. polon. Math. 81, No. 2, 111-122 (2003) · Zbl 1036.46030 · doi:10.4064/ap81-2-2
[15]Pinasco, D.: Lp-representable functions on Banach spaces, J. math. Anal. appl. 335, 480-497 (2007) · Zbl 1127.46032 · doi:10.1016/j.jmaa.2007.01.088
[16]Hervé, M.: Analyticity in infinite dimensional spaces, De gruyter stud. In math. 10 (1989) · Zbl 0666.58008