Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions

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1. [1] A. Atzmon, Operators which are annihilated by analytic functions and invariant subspaces, Acta Math. 144 (1980), 27-63. Zbl0449.47007
2. [2] A. Atzmon, Operators with resolvent of bounded characteristic, Integral Equations Oper. Theory 6 (1983), 779-802. 
3. [3] C. Bennett and J. E. Gilbert, Homogeneous algebras on the circle: I--Ideals of analytic functions, Ann. Inst. Fourier (Grenoble) 22 (3) (1972), 1-19. Zbl0228.46046
4. [4] L. Carleson, Sets of uniqueness of functions regular in the unit circle, Acta Math. 87 (1952), 325-345. Zbl0046.30005
5. [5] I. Domar, On the analytic transform of bounded linear functionals on certain Banach algebras, Studia Math. 53 (1975), 203-224. Zbl0272.46030
6. [6] R. G. Douglas, H. S. Shapiro and A. L. Shields, Cyclic vectors and invariant subspaces for the backward shift operator, Ann. Inst. Fourier (Grenoble) 20 (1) (1970), 37-76. Zbl0186.45302
7. [7] J. Esterle, Quasimultipliers, representations of $H^{\infty }$, and the closed ideal problem for commutative Banach algebras, in: Lecture Notes in Math. 975, Springer, 1983, 66-162. 
8. [8] J. Esterle, Distributions on Kronecker sets, strong forms of uniqueness, and closed ideals of $A^{+}$, J. Reine Angew. Math. 450 (1994), 43-82. 
9. [9] J. Esterle, Uniqueness, strong forms of uniqueness and negative powers of contractions, in: Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., 1994, 127-145. Zbl0893.46043
10. [10] J. Esterle, M. Rajoelina and M. Zarrabi, On contractions with spectrum contained in the Cantor set, Math. Proc. Cambridge Philos. Soc. 117 (1995), 339-343. Zbl0830.47001
11. [11] J. Esterle, E. Strouse and F. Zouakia, Closed ideals of the algebra of absolutely convergent Taylor series, Bull. Amer. Math. Soc. 31 (1994), 39-43. Zbl0803.46052
12. [12] J. Esterle, E. Strouse and F. Zouakia, Closed ideals of $A^{+}$ and the Cantor set, J. Reine Angew. Math. 449 (1994), 65-79. Zbl0791.46027
13. [13] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, Berlin, 1979. Zbl0439.43001
14. [14] V. P. Gurariĭ, Harmonic analysis in spaces with a weight, Trans. Moscow Math. Soc. 35 (1979), 21-75. 
15. [15] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962. Zbl0117.34001
16. [16] J. P. Kahane, Séries de Fourier absolument convergentes, Ergeb. Math. Grenzgeb. 50, Springer, Berlin, 1970. 
17. [17] J. P. Kahane, Idéaux fermés dans certaines algèbres de fonctions analytiques, in: Lecture Notes in Math. 336, Springer, 1973, 5-14. 
18. [18] J. P. Kahane et R. Salem, Ensembles parfaits et séries trigonométriques, Hermann, Paris, 1963. Zbl0112.29304
19. [19] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York, 1968. 
20. [20] K. Kellay, Synthèse des hyperdistributions à coefficients de Fourier négatifs bornés, in preparation. 
21. [21] B. Korenblyum, Closed ideals in the ring $A^n$, Functional Anal. Appl. 6 (1972), 203-214. 
22. [22] A. L. Matheson, Closed ideals in rings of analytic functions satisfying a Lipschitz condition, in: Lecture Notes in Math. 604, Springer, 1976, 67-72. 
23. [23] I. I. Privalov, Randeigenschaften analytischer Funktionen, Zweite Aufl., Deutsch. Verlag Wiss., Berlin, 1956. 
24. [24] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. 
25. [25] B. A. Taylor and D. L. Williams, Ideals in rings of analytic functions with smooth boundary values, Canad. J. Math. 22 (1970), 1266-1283. Zbl0204.44302
26. [26] G. S. Tumarkin, Description of a class of functions approximable by rational functions with fixed poles, Izv. Akad. Nauk Armyansk. SSR 2 (1966), 89-105 (in Russian). 
27. [27] M. Zarrabi, Synthèse spectrale dans certaines algèbres de Beurling sur le cercle unité, Bull. Soc. Math. France 118 (1990), 241-249. 
28. [28] M. Zarrabi, Contractions à spectre dénombrable et propriétés d'unicité des fermés dénombrables du cercle, Ann. Inst. Fourier (Grenoble) 43 (1) (1993), 251-263. 
29. [29] E. H. Zerouali, Synthèse spectrale dans une certaine limite projective d'algèbres de Beurling, Ann. Sci. Math. Québec 16 (1992), 109-115. 
30. [30] E. H. Zerouali, Ensembles universels de synthèse pour les algèbres de Beurling, Bull. Sci. Math. (2) 118 (1994), 209-223. 

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