Open AccessBeurling’s phenomenon on analytic Hilbert spaces over the complex plane
Author(s) -
Shuyun Wei
Publication year - 2009
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-09-10196-x
Subject(s) - algorithm , linear subspace , artificial intelligence , annotation , computer science , mathematics , geometry
In this paper, we show that Beurling’s theorem on analytic Hilbert spaces over the complex plane analogous to the Hardy space or the Bergman space does not hold, but for finite co-dimensional quasi-invariant subspaces, they are generated by their wandering subspace if and only if they are generated by z n z^n provided that the order of the reproducing kernels K λ ( z ) K_\lambda (z) is less than 2 but not equal to 1.