| Abstract |
The first singular, non-atomic, spectral measure was constructed by Jorgensen and Pedersen. They proved that 1/R-Cantor measure $\mu_R$is a spectral measure with a spectrum $\Lambda$ if R is even。For any square integral function $f$,
Let, $F_{f, \Lambda}=\sum_{\lambda\in\Lambda}f^(\lambda)z^{\lambda}$.
Hence, H={F_{f, \Lambda}: f a is square integral function}
is a complete subspace of Hardy space. In this talk, we mainly investigated the following problems:
(1) Integral representation theorem of H; (2) Growth theorem of H；(3) Strichartz’s exceptional set and Carleson’s exceptional set under certain conditions;(4) Picard property, Cantor boundary behaviour of $F_{f,\Lambda}$, under Hadamard gap condition.
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