The characterization of the almost periodic ultradistributions of Beurling type. (English) Zbl 0765.46021
The space of almost periodic ultradistributions of Beurling type is introduced and studied. A structure theorem for the bounded ultradistributions is given as well as an application to the Dirichlet problem for the half plane with almost periodic ultradistributional boundary values.
Reviewer: D.Zarnadze (Tbilisi)
MSC:
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
| 46F15 | Hyperfunctions, analytic functionals |
Keywords:
space of almost periodic ultradistributions of Beurling type; structure theorem for the bounded ultradistributions; Dirichlet roblem for the half plane with almost periodic ultradistributional boundary valuesReferences:
| [1] | Chin Cheng Chow, La transformation de Fourier complexe et l’équation de convolution, Chinese J. Math. 1 (1973), no. 1, 3 – 112 (French). · Zbl 0367.46035 |
| [2] | Ioana Cioranescu and László Zsidó, \?-ultradistributions and their application to operator theory, Spectral theory (Warsaw, 1977) Banach Center Publ., vol. 8, PWN, Warsaw, 1982, pp. 77 – 220. |
| [3] | C. Corduneanu, Almost periodic functions, 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; Interscience Tracts in Pure and Applied Mathematics, No. 22. · Zbl 0672.42008 |
| [4] | Hikosaburo Komatsu, Ultradistributions. I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 25 – 105. · Zbl 0258.46039 |
| [5] | J. Körner, Roumieu’sche Ultradistributionen als Randverteilung holomorpher funktionen, Dissertation, Kiel, 1975. |
| [6] | 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). , https://doi.org/10.1007/BF01310050 Hans-Joachim Petzsche, Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. II, Manuscripta Math. 27 (1979), no. 3, 221 – 251 (German, with English summary). · Zbl 0393.46032 · doi:10.1007/BF01309009 |
| [7] | S. Pilipović, Hilbert transformation of Beurling ultradistributions, Rend. Sem. Mat. Univ. Padova 77 (1987), 1 – 13. · Zbl 0636.46043 |
| [8] | L. Schwartz, Théorie des distributions, Hermann, Paris, 1973. |
| [9] | Yoshiko Taguchi, Fourier coefficients of periodic functions of Gevrey classes and ultradistributions, Yokohama Math. J. 35 (1987), no. 1-2, 51 – 60. · Zbl 0649.46039 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
