Almost periodic ultradistributions of Beurling and of Roumieu type
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- by M. C. Gómez-Collado
- Proc. Amer. Math. Soc. 129 (2001), 2319-2329
- DOI: https://doi.org/10.1090/S0002-9939-00-05806-8
- Published electronically: December 28, 2000
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Abstract:
We characterize the almost periodic ultradistributions of Beurling and of Roumieu type in terms of classical Bohr almost periodicity. Then we study the Fourier series associated with such an ultradistribution.References
- Luigi Amerio and Giovanni Prouse, Almost-periodic functions and functional equations, Van Nostrand Reinhold Co., New York-Toronto-Melbourne, 1971. MR 0275061, DOI 10.1007/978-1-4757-1254-4
- Göran Björck, Linear partial differential operators and generalized distributions, Ark. Mat. 6 (1966), 351–407 (1966). MR 203201, DOI 10.1007/BF02590963
- Rüdiger W. Braun, An extension of Komatsu’s second structure theorem for ultradistributions, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40 (1993), no. 2, 411–417. MR 1255048
- R. W. Braun, R. Meise, and B. A. Taylor, Ultradifferentiable functions and Fourier analysis, Results Math. 17 (1990), no. 3-4, 206–237. MR 1052587, DOI 10.1007/BF03322459
- Ioana Cioranescu, The characterization of the almost periodic ultradistributions of Beurling type, Proc. Amer. Math. Soc. 116 (1992), no. 1, 127–134. MR 1111214, DOI 10.1090/S0002-9939-1992-1111214-5
- Ioana Cioranescu, Asymptotically almost periodic distributions, Appl. Anal. 34 (1989), no. 3-4, 251–259. MR 1387173, DOI 10.1080/00036818908839898
- C. Corduneau, Almost periodic functions, Tracts in Pure Appl. Math. 22, Interscience, New York (1968).
- Hikosaburo Komatsu, Ultradistributions. I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 25–105. MR 320743
- Michael Langenbruch, Surjective partial differential operators on spaces of ultradifferentiable functions of Roumieu type, Results Math. 29 (1996), no. 3-4, 254–275. MR 1387567, DOI 10.1007/BF03322223
- Reinhold Meise and B. Alan Taylor, Whitney’s extension theorem for ultradifferentiable functions of Beurling type, Ark. Mat. 26 (1988), no. 2, 265–287. MR 1050108, DOI 10.1007/BF02386123
- Raghavan Narasimhan, Analysis on real and complex manifolds, 2nd ed., Advanced Studies in Pure Mathematics, Vol. 1, Masson & Cie, Éditeurs, Paris; North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. MR 0346855
- Stevan Pilipović, Characterizations of bounded sets in spaces of ultradistributions, Proc. Amer. Math. Soc. 120 (1994), no. 4, 1191–1206. MR 1211587, DOI 10.1090/S0002-9939-1994-1211587-0
- Stevan Pilipović, Structural theorems for ultradistributions, Dissertationes Math. (Rozprawy Mat.) 340 (1995), 223–235. Different aspects of differentiability (Warsaw, 1993). MR 1342581
- Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
Bibliographic Information
- M. C. Gómez-Collado
- Affiliation: Departamento de Matemática Aplicada, E.T.S. Arquitectura, Camino de Vera, E-46071 Valencia, Spain
- Email: cgomezc@mat.upv.es
- Received by editor(s): August 17, 1999
- Received by editor(s) in revised form: November 30, 1999
- Published electronically: December 28, 2000
- Additional Notes: The author thanks C. Fernández and A. Galbis for guidance and encouragement during the preparation of her thesis, of which this work forms a part.
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2319-2329
- MSC (2000): Primary 46F05
- DOI: https://doi.org/10.1090/S0002-9939-00-05806-8
- MathSciNet review: 1823915