Geodesic
Hilbert spaces of analytic functions of infinitely many variables
O. V. Lopushansky1 ; A. V. Zagorodnyuk2
1 Institute of Mathematics Cracow University of Technology Warszawska 24 31-155 Kraków, Poland
2 Institute for Applied Problems of Mechanics and Mathematics Ukrainian Academy of Sciences 3b, Naukova St. 79053, Lviv, Ukraine
Annales Polonici Mathematici, Tome 81 (2003) no. 2, pp. 111-122

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space $H^2$ on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.
DOI : 10.4064/ap81-2-2
Keywords: study spaces analytic functions generated homogeneous polynomials dual space symmetric hilbertian tensor product hilbert space particular introduce analogue classical hardy space hilbert unit ball investigate spectral decomposition unitary operators space prove wiener type theorem algebra analytic functions hilbert unit ball

O. V. Lopushansky 1 ; A. V. Zagorodnyuk 2

1 Institute of Mathematics Cracow University of Technology Warszawska 24 31-155 Kraków, Poland
2 Institute for Applied Problems of Mechanics and Mathematics Ukrainian Academy of Sciences 3b, Naukova St. 79053, Lviv, Ukraine 
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O. V. Lopushansky; A. V. Zagorodnyuk. Hilbert spaces of analytic functions
 of infinitely many variables. Annales Polonici Mathematici, Tome 81 (2003) no. 2, pp. 111-122. doi: 10.4064/ap81-2-2

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