Spectral synthesis of functions of bounded variation
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- by Aharon Atzmon PDF
- Proc. Amer. Math. Soc. 47 (1975), 417-422 Request permission
Abstract:
It is proved that every bounded measurable function on $( - \infty ,\infty )$ which for some constant $a > 0$ is of bounded variation on $( - \infty , - a)$ and on $(a,\infty )$, admits spectral synthesis in the weak-star topology of ${L^\infty }( - \infty ,\infty )$.References
- G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
- Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482
- Paul Malliavin, Sur l’impossibilité de la synthèse spectrale dans une algèbre de fonctions presque périodiques, C. R. Acad. Sci. Paris 248 (1959), 1756–1759 (French). MR 107127
- Harry Pollard, The harmonic analysis of bounded functions, Duke Math. J. 20 (1953), 499–512. MR 57363
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 417-422
- DOI: https://doi.org/10.1090/S0002-9939-1975-0352880-1
- MathSciNet review: 0352880