Results 101 to 110 of about 370 (125)
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Bolletino Della Unione Mathematica Italiana. Ser. B, 1988
Let \(S^{\alpha,0}_{\alpha,0}\) be the Gelfand space with the sequences of norms \(\{\beta_ k^{\alpha}(\phi)\}=\{\| \sup_{m,n\in {\mathbb{N}}_ 0}\{C^{\alpha}_{k,m,n}| x^ m\phi^{(n)}(x)| \}\|_{\infty}\}\). Here \({\mathbb{N}}_ 0={\mathbb{N}}\cup \{0\}\) is the set of nonnegative integers and \(C^{\alpha}_{k,m,n}=(k^{m+n})/(m^{\alpha m}n^{\alpha n ...
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Let \(S^{\alpha,0}_{\alpha,0}\) be the Gelfand space with the sequences of norms \(\{\beta_ k^{\alpha}(\phi)\}=\{\| \sup_{m,n\in {\mathbb{N}}_ 0}\{C^{\alpha}_{k,m,n}| x^ m\phi^{(n)}(x)| \}\|_{\infty}\}\). Here \({\mathbb{N}}_ 0={\mathbb{N}}\cup \{0\}\) is the set of nonnegative integers and \(C^{\alpha}_{k,m,n}=(k^{m+n})/(m^{\alpha m}n^{\alpha n ...
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Ultradistributions and Time-Frequency Analysis
2006The aim of the paper is to show the connection between the theory of ultradistributions and time-frequency analysis. This is done through time-frequency representations and modulation spaces. Furthermore, some classes of pseudo-differential operators are observed.
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Hyperfunctions, Ultradistributions and Microfunctions
1993As exemplified in the introduction of L. Schwartz’ book [24] individual generalized functions had been known before he introduced the distributions D′ (Ω) in 1948–51. Dirac’s δ function and Hadamard’s finite part of x + α , α < -1, are famous. More generally P. Levy [16] had determined the dual of C m ([a, b]).
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On the structure of certain ultradistributions
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2009Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f, 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP2Nk 0 D"a"f "a".
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Hypoellipticity in ultradistribution spaces
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics = 東京大学理学部紀要. 第1類A, 数学, 1987In the previous papers by the author, \textit{S. Hashimoto} and \textit{Y. Morimoto} [Commun. Partial Differ. Equations 8, 1277-1289 (1983; Zbl 0525.35086)] and by the author [Gevrey hypoellipticity of a class of pseudodifferential operators (to appear in Tôhoku Math. J.)], we have considered Gevrey hypoellipticity of a pseudodifferential equation \((1)
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Ultradistributions. III: Vector valued ultradistributions and the theory of kernels
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics = 東京大学理学部紀要. 第1類A, 数学, 1982openaire +2 more sources
A sequential approach to the convolution of Roumieu ultradistributions
Advances in Operator Theory, 2020Svetlana Mincheva-Kaminska
exaly
Beurling ultradistributions of Lp-growth
Journal of Mathematical Analysis and Applications, 2003Antonio Galbis
exaly