The characterization of the almost periodic ultradistributions of Beurling type
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- by Ioana Cioranescu PDF
- Proc. Amer. Math. Soc. 116 (1992), 127-134 Request permission
Abstract:
We introduce and study the space of almost periodic ultradistributions of Beurling type and characterize it in terms of classical Bohr almost periodicity. To this aim we establish a structure theorem for the bounded ultradistributions. Application is made to the Dirichlet Problem for the half plane with almost periodic untradistributional boundary values.References
- Chin Cheng Chow, La transformation de Fourier complexe et l’équation de convolution, Chinese J. Math. 1 (1973), no. 1, 3–112 (French). MR 383071
- Ioana Cioranescu and László Zsidó, $\omega$-ultradistributions and their application to operator theory, Spectral theory (Warsaw, 1977) Banach Center Publ., vol. 8, PWN, Warsaw, 1982, pp. 77–220. MR 738280
- C. Corduneanu, Almost periodic functions, Interscience Tracts in Pure and Applied Mathematics, No. 22, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1968. With the collaboration of N. Gheorghiu and V. Barbu; Translated from the Romanian by Gitta Bernstein and Eugene Tomer. MR 0481915
- Hikosaburo Komatsu, Ultradistributions. I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 25–105. MR 320743 J. Körner, Roumieu’sche Ultradistributionen als Randverteilung holomorpher funktionen, Dissertation, Kiel, 1975.
- Hans-Joachim Petzsche, Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. I, Manuscripta Math. 24 (1978), no. 2, 133–171 (German, with English summary). MR 492653, DOI 10.1007/BF01310050
- S. Pilipović, Hilbert transformation of Beurling ultradistributions, Rend. Sem. Mat. Univ. Padova 77 (1987), 1–13. MR 904609 L. Schwartz, Théorie des distributions, Hermann, Paris, 1973.
- Yoshiko Taguchi, Fourier coefficients of periodic functions of Gevrey classes and ultradistributions, Yokohama Math. J. 35 (1987), no. 1-2, 51–60. MR 928372
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 127-134
- MSC: Primary 46F05; Secondary 46F10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1111214-5
- MathSciNet review: 1111214