Abstract
The article is devoted to the problem of Hilbert–Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary group endowed with an invariant probability measure. Reproducing kernels of Hardy spaces, integral formulas of analytic extensions and their boundary values are considered.
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Berezanski Yu.M., Kondratiev Yu.G.: Spectral Methods in Infinite-Dimensional Analysis. Springer, Berlin (1995)
Borodin A., Olshanski G.: Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Ann. Math. 161, 1319–1422 (2005)
Borodin A.: Determinantal point processes. In: Akemann, G., Baik, J., Di Francesco, P. (eds.) Oxford Handbook of Random Matrix Theory, Oxford Univ. Press, Oxford (2011)
Carando D., Dimant V., Muro S.: Coherent sequences of polynomial ideals on Banach spaces. Math. Nachr. 282(8), 1111–1133 (2009)
Cole B., Gamelin T.W.: Representing measures and Hardy spaces for the infinite polydisk algebra. Proc. Lond. Math. Soc. 53, 112–142 (1986)
Dwyer III T.A.W.: Partial differential equations in Fischer–Fock spaces for the Hilbert–Schmidt holomorphy type. Bull. Am. Math. Soc. 77(5), 725–739 (1971)
Gamelin T.W.: Analytic functions on Banach spaces. In: Gauthier, P.M., Sabidussi, G. (eds.) Complex Function Theory, pp. 87–223. Kluwer, Dordrecht (1994)
Floret K.: Natural norms on symmetric tensor products of normed spaces. Note di Matematica 17, 153–188 (1997)
Hervé M.: Analyticity in Infiite Dimensional Spaces, de Gruyter Stud. in Math., vol. 10. Walter de Gruyter, Berlin (1989)
Hewitt E., Ross K.A.: Abstract Harmonic Analysis, vol. 2. Springer, Berlin (1994)
Lopushansky O.: Hardy type space associated with an infinite-dimensional unitary matrix group. Abst. Appl. An. ID 810735, 1–7 (2013)
Neretin Yu.A.: Hua type integrals over unitary groups and over projective limits of unitary groups. Duke Math. J. 114(2), 239–266 (2002)
Olshanski G.: The problem of harmonic analysis on the infinite-dimensional unitary group. J. Funct. Anal. 205, 464–524 (2003)
Neeb, K.H., Ørted, B.: Hardy spaces in an infinite dimensional setting. In: Doebner, H.D. (ed.) Lie Theory and Its Applications in Physics, pp. 3–27. Word Sci. Publ., Singapore (1998)
Petersson P.: Hypercyclic convolution operators on entire functions of Hilbert–Schmidt holomorphy type. Ann. Math. Blaise Pascal 8(2), 107–114 (2001)
Pickrell D.: Measures on infinite-dimensional Grassmann manifolds. J. Funct. Anal. 70, 323–356 (1987)
Pinasco D., Zalduendo I.: Integral representations of holomorphic functions on Banach spaces. J. Math. Anal. Appl. 308, 159–174 (2005)
Rudin W.: Function Theory in the Unit Ball of \({\mathbb{C}^{n}}\). Springer, Berlin (2008)
Saitoh, S.: Integral Transforms, Reproducing Kernels and Their Applications. Pitman Research Notes in Math. Ser., vol. 369. Longman (1997)
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Lopushansky, O. The Hilbert–Schmidt Analyticity Associated with Infinite-Dimensional Unitary Groups. Results Math 71, 111–126 (2017). https://doi.org/10.1007/s00025-016-0549-4
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DOI: https://doi.org/10.1007/s00025-016-0549-4