Matsuzawa, Tadato A calculus approach to hyperfunctions. I. (English) Zbl 0636.46047 Nagoya Math. J. 108, 53-66 (1987). Der Verf. zeigt, daß sich Hyperfunktionen als Randwerte von Lösungen der Wärmeleitungsgleichung darstellen lassen und benutzt diese Darstellung zum Beweis des Paley-Wiener Satzes und eines Regularitätssatzes. Eine analoge Darstellung durch Lösungen von elliptischen Differentialgleichungen wurde vom Ref. [Math. Z. 96, 373-392 (1967; Zbl 0144.357)] zum Beweis eines Regularitätssatzes verwendet. M. Langenbruch hat Darstellungen von Distributionen als Randwerte von hypoelliptischen Gleichungen untersucht [vgl. Manuscripta Math. 26, 17-35 (1978; Zbl 0391.35017)]. Reviewer: G.Bengel Cited in 6 ReviewsCited in 19 Documents MSC: 46F15 Hyperfunctions, analytic functionals 46F20 Distributions and ultradistributions as boundary values of analytic functions 35K05 Heat equation 65H10 Numerical computation of solutions to systems of equations Keywords:hyperfunctions; heat-equation; Paley-Wiener theorem Citations:Zbl 0144.357; Zbl 0391.35017 PDFBibTeX XMLCite \textit{T. Matsuzawa}, Nagoya Math. J. 108, 53--66 (1987; Zbl 0636.46047) Full Text: DOI References: [1] (1978) [2] J. Fac. Sci. Univ. Tokyo, Sect. IA 24 pp 607– (1977) [3] J. Fac. Sci. Univ. Tokyo, Sect. IA 20 pp 25– (1973) [4] In Sem. on microlocal analysis pp 3– (1979) [5] Les hyperfonctions de M. Sato, Sém. Bourbaki 1960–1961 [6] Proc. Symp. Pure Math 83 pp 129– (1966) [7] DOI: 10.1080/03605308308820303 · Zbl 0525.35086 · doi:10.1080/03605308308820303 [8] Introduction to pseudodifferential and Fourier integral operators, I (1981) [9] to appear in J. Fac. Sci. Univ [10] The analysis of linear partial differential operators, I (1983) 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.