Rendiconti del Circolo Matematico di Palermo

, Volume 51, Issue 3, pp 403–410 | Cite as

Bounded analytic structure of the banach space of formal power series

  • B. Yousefi


Let\(\{ \beta (n)\} _{n = 0}^\infty \) be a sequence of positive numbers and 1≤p<∞. We consider the spaceH p(β) of all power series\(f(z) = \sum\limits_{n = 0}^\infty {\hat f(n)z^n } \) such that Σ|\(\Sigma |\hat f(n)|^p \beta (n)^p< \infty \)(n)|p β(n p<∞. We investigate regions on which our formal power series represent bounded analytic functions.

AMS Subject Classification

Primary 47B37 Secondary 47A25 

Keywords and phrases

The Banach space of formal power series associated with a sequenceβ reproducing kernel bounded point evaluation Caratheodory region 


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  1. [1]
    Gamelin T.,Uniform algebras, Chelsea, New York, 1984.Google Scholar
  2. [2]
    Seddighi K., Hedayatiyan K., Yousefi B.,Operators acting on certain Banach spaces of analytic functions, International Journal of Mathematics and Mathematical Sciences,18 (1995), 107–110.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Shields A. L.,Weighted shift operators and analytic function theory, Math. Survey, A.M.S. Providence,13 (1974), 49–128.MathSciNetGoogle Scholar
  4. [4]
    Yousefi B.,On the space ℓ p(β), Rend. Circ. Mat. Palermo,49 (2000), 115–120.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer 2002

Authors and Affiliations

  • B. Yousefi
    • 1
  1. 1.Dep. of Math. College of SciencesShiraz UniversityShirazIran

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