Abstract
Let Ω be a nonempty open set of thek-dimensional euclidean space \( \mathbb{R}^k \). In this paper, we give a structure theorem on the ultradistributions of Beurling type in Ω. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in Ω.
Resumen
Sea Ω un abierto no vacío del espacio euclídeok-dimensional \( \mathbb{R}^k \). En este artículo se obtiene un teorema de estructura de las ultradistribuciones de Beurling definidas en Ω. También se obtienen otros resultados de estructura de ciertas ultradistribuciones, en términos de medidas complejas definidas en Ω.
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References
Komatsu, H., (1973). Ultradistributions I. Structure theorems and characterizations,J. Fac. Sci. Uni. Tokyo,20, 25–105.
Rudin, W., (1970).Real and Complex Analysis, McGraw-Hill, London New York.
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Valdivia, M. On the structure of the ultradistributions of Beurling type. Rev. R. Acad. Cien. Serie A. Mat. 102, 221–235 (2008). https://doi.org/10.1007/BF03191823
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DOI: https://doi.org/10.1007/BF03191823
Keywords
- Banach space
- complex Borel measures
- locally convex spaces
- projective limit
- strong topology
- Radon measure
- ultradifferentiable functions
- ultradistributions of Beurling type