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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.
46E50Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
42B30$H^p$-spaces (Fourier analysis)
46G20Infinite dimensional holomorphy
46J15Banach algebras of differentiable or analytic functions, $H^p$-spaces
Full Text: DOI
[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 · 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) · Zbl 0495.32001
[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) · Zbl 1034.46504
[12] Gamelin, T. W.: Uniform algebras, (1984) · Zbl 0213.40401
[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