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Validity of Closed Ideals in Algebras of Series of Square Analytic Functions

Musa Siddig1* and Shawgy Hussien2

1Department of Mathematics, Faculty of Science, University of Kordofan, Sudan .

2Department of Mathematics, College of Science, Sudan University of Science and Technology, Sudan .

Corresponding author Email: muss.yousif3@gmail.com

DOI: http://dx.doi.org/10.13005/OJPS04.02.05

We show the validity of a complete description of closed ideals of the algebra  is the algebra of series of analytic functions satisfying the Lipschitz condition of order αj2 obtained by.15


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Siddig M, Hussien S. Validity of Closed Ideals in Algebras of Series of Square Analytic Functions. Oriental Jornal of Physical Sciences 2019; 4(2). DOI:http://dx.doi.org/10.13005/OJPS04.02.05

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Siddig M, Hussien S. Validity of Closed Ideals in Algebras of Series of Square Analytic Functions. Oriental Jornal of Physical Sciences 2019; 4(2). Available From : https://bit.ly/3qfhxG4


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Received: 12-01-2020
Accepted: 05-02-2020


























This completes the proof of the lemma.

Conclusion. Now, according to (18) and Lemmas (4.4), (4.5) and (4.8), we obtain

This completes the proof of Theorem (2.1)

References

  1. B. Bouya, Id´eaux ferm´es de certaines alg`ebres de fonctions analytiques, C. R. Math. Acad. Sci. Paris 343 (2006), no. 4, 235–238.
  2. L. Carleson, A representation formula in the Dirichlet space, Math. Z. 73 (1960), 190–196.
  3. P. L.Duren, Theory of Hp spaces, Academic Press, New York, 1970.
  4. O.El-Fallah, K. Kellay, T. Ransford, Cyclicity in the Dirichlet space, Ark. Mat. 44 (1) (2006), 61–86.
  5. J. Esterle, E. Strouse, F. Zouakia, Closed ideal of A+ and the Cantor set, J. reine angew. Math. 449 (1994), 65–79.
  6. H. Hedenmalm, A. Shields, Invariant subspaces in Banach spaces of ana- lytic functions, Mich. Math. J. 37 (1990), 91–104.
  7. K. Hoffman, Banach spaces of analytic functions, Dover Publications Inc., New York, 1988, Reprint of the 1962 original.
  8. B. I. Korenblum, Invariant subspaces of the shift operator in a weighted Hilbert space, Mat. Sb. 89(131)(1972), 110–138.
  9. A. Matheson, Approximation of analytic functions satisfying a Lipschitz condition, Mich. Math. J. 25 (1978), no. 3, 289–298.
  10. W. Rudin, Real and complex analysis, second ed., McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York, 1974.
  11. F. A. Shamoyan, Closed ideals in algebras of functions that are analytic in the disk and smooth up to its boundary, Mat. Sb. 79 (1994), no. 2, 425–445. CLOSED IDEALS IN SOME ALGEBRAS OF ANALYTIC FUNCTIONS 19
  12. N. A. Shirokov, Analytic functions smooth up to the boundary, Lecture Notes in Mathematics, 1312. Springer-Verlag, Berlin, 1988.
  13. N. A. Shirokov, Closed ideals of algebras of B_ pq–type, (Russian) Izv. Akad. Nauk. SSSR, Mat. 46 (1982), no. 6, 1316–1333.
  14. B. A. Taylor, D.L. Williams, Ideals in rings of analytic functions with smooth boundary values, Can. J. Math. 22 (1970), 1266–1283. E-mail address: brahimbouya@gmail.com
  15. Brahim Bouya ,Closed ideals in some algebras of analytic function, arXiv:0802.0890v1 [math.CV] 6 Feb 2008.
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