$H^{\infty }(R)+AP$ is closed
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- by Stephen Power
- Proc. Amer. Math. Soc. 65 (1977), 73-76
- DOI: https://doi.org/10.1090/S0002-9939-1977-0448047-0
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Abstract:
Let ${H^\infty }(R)$ be the space of functions on the real line R which are boundary functions of functions bounded and analytic in the upper half-plane and let AP denote the space of uniformly almost periodic functions on R. We show that ${H^\infty }(R) + AP$ is closed and is not an algebra.References
- A. S. Besicovitch, Almost periodic functions, Dover Publications, Inc., New York, 1955. MR 0068029
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496, DOI 10.1007/978-1-4419-8638-2
- Walter Rudin, Spaces of type $H^{\infty }+C$, Ann. Inst. Fourier (Grenoble) 25 (1975), no. 1, vi, 99–125 (English, with French summary). MR 377520
- Donald Sarason, Generalized interpolation in $H^{\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 208383, DOI 10.1090/S0002-9947-1967-0208383-8 —, Functions of vanishing mean oscillation (preprint).
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 73-76
- MSC: Primary 46E15; Secondary 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1977-0448047-0
- MathSciNet review: 0448047