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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On certain bounded solutions of $g\ast \mu =f$
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by A. M. Fink and W. R. Madych PDF
Proc. Amer. Math. Soc. 75 (1979), 235-242 Request permission

Abstract:

We show that, under certain conditions, bounded solutions g of $g \ast \mu = f$ are asymptotically almost periodic.
References
  • Arne Beurling, Sur une classe de fonctions presque-périodiques, C. R. Acad. Sci. Paris 225 (1947), 326–328 (French). MR 21146
  • A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799
  • G. S. Jordan and Robert L. Wheeler, Linear integral equations with asymptotically almost periodic solutions, J. Math. Anal. Appl. 52 (1975), no. 3, 454–464. MR 410311, DOI 10.1016/0022-247X(75)90072-4
  • W. R. Madych, Absolute summability of Fourier transforms on $R^{n}$, Indiana Univ. Math. J. 25 (1976), no. 5, 467–479. MR 410253, DOI 10.1512/iumj.1976.25.25037
  • Richard K. Miller, Nonlinear Volterra integral equations, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Menlo Park, Calif., 1971. MR 0511193
  • N. M. Rivière, The Fourier method in approximation theory (unpublished lecture notes).
  • Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 75 (1979), 235-242
  • MSC: Primary 45A05; Secondary 45M05
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0532143-5
  • MathSciNet review: 532143