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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(e) ISSN 1061-0022(p)

     

Uniform subalgebras of $ L^{\infty}$ on the unit circle generated by almost periodic functions

Author(s): A. Brudnyi; D. Kinzebulatov
Original publication: Algebra i Analiz, tom 19 (2007), nomer 4.
Journal: St. Petersburg Math. J. 19 (2008), 495-518.
MSC (2000): Primary 30H05; Secondary 46J20
Posted: May 9, 2008
MathSciNet review: 2381931
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Abstract | References | Similar articles | Additional information

Abstract: Analogs of almost periodic functions for the unit circle are introduced. Certain uniform algebras generated by such functions are studied, the corona theorems for them are proved, and their maximal ideal spaces are described.


References:

[B]
H. Bohr, Almost periodic functions, Chelsea Publ. Co., New York, 1947. MR 0020163 (8:512a)

[Br]
A. Brudnyi, Topology of the maximal ideal space of $ H^{\infty}$, J. Funct. Anal. 189 (2002), no. 1, 21-52. MR 1887628 (2003c:46066)

[Bö]
A. Böttcher, On the corona theorem for almost periodic functions, Integral Equations Operator Theory 33 (1999), no. 3, 253-272. MR 1671480 (2000b:46086)

[D]
J. Dieudonné, Foundations of modern analysis, Pure Appl. Math., vol. 10-I, Acad. Press, New York-London, 1969. MR 0349288 (50:1782)

[G]
J. Garnett, Bounded analytic functions, Pure Appl. Math., vol. 96, Acad. Press, New York-London, 1981. MR 0628971 (83g:30037)

[H]
F. Hirzebruch, Topological methods in algebraic geometry, Grundlehren Math. Wiss., Bd. 131, Springer-Verlag New York, Inc., New York, 1966. MR 0202713 (34:2573)

[JT]
B. Jessen and H. Tornehave, Mean motions and zeros of almost periodic functions, Acta Math. 77 (1945), 137-279. MR 0015558 (7:438d)

[L]
E. Lindelöf, Sur une principe générale de l'analyse et ces applications à la théorie de la representation conforme, Acta Soc. Sci. Fenn. 46 (1915).

[LZ]
B. M. Levitan and V. V. Zhikov, Almost periodic functions and differential equations, Moskov. Gos. Univ., Moscow, 1978; English transl., Cambridge Univ. Press, Cambridge-New York, 1982. MR 0509035 (80d:42010); MR 0690064 (84g:34004)

[P]
L. S. Pontryagin, Selected works. Vol. 2. Topological groups, Gordon and Breach Sci. Publ., New York, 1986. MR 0898007 (90a:01106)

[R]
H. Royden, Function algebras, Bull. Amer. Math. Soc. 69 (1963), 281-298. MR 0149327 (26:6817)

[S]
D. Sarason, Toeplitz operators with semi-almost periodic symbols, Duke Math. J. 44 (1977), 357-364. MR 0454717 (56:12965)

[Sp]
I. Spitkovskiĭ, Factorization of triangular matrix-functions with diagonal elements of the class $ {SAP}_{\,\Gamma}$, Proceedings of a Commemorative Seminar on Boundary Value Problems (Minsk, 1981), ``Universitetskoe'', Minsk, 1985, pp. 188-192. (Russian) MR 0873569


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Additional Information:

A. Brudnyi
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
Email: albru@math.ucalgary.ca

D. Kinzebulatov
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

DOI: 10.1090/S1061-0022-08-01007-8
PII: S 1061-0022(08)01007-8
Keywords: Bounded holomorphic function, almost periodic function, uniform algebra, maximal ideal space, corona theorem
Received by editor(s): 9/NOV/2006
Posted: May 9, 2008
Additional Notes: Supported in part by NSERC
Copyright of article: Copyright 2008, American Mathematical Society




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