Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE HILBERT SPACE OF FORMAL POWER SERIES

  • YOUSEFI, Bahman (Department of Mathematics College of Sciences Shiraz University) ;
  • SOLTANI, Rahmat (Department of Mathematics Shiraz Payam-e-noor University)
  • Received : 2004.06.28
  • Published : 2004.09.25
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Abstract

Let $\{{\beta}(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers such that ${\beta}(0)=1$. We consider the space $H^2({\beta})$ of all power series $f(z)=^{Po}_{n=0}{\hat{f}}(n)z^n$ such that $^{Po}_{n=0}{\mid}{\hat{f}}(n){\mid}^2{\beta}(n)^2<{\infty}$. We link the ideas of subspaces of $H^2({\beta})$ and zero sets. We give some sufficient conditions for a vector in $H^2({\beta})$ to be cyclic for the multiplication operator $M_z$. Also we characterize the commutant of some multiplication operators acting on $H^2({\beta})$.

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References

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