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Hypoellipticity in ultradistribution spaces
Hypoellipticity in ultradistribution spacesapplication ...
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GENERALIZED ROUMIEU TEMPERED ULTRADISTRIBUTIONS
Poincare Journal of Analysis and Applications, 2022 openaire +1 more source
Ultradistributions of semigroups
Sibirskij Matematiceskij Zurnal, 2012 Kostić, Marko, Pilipović, Stevan
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Microlocal Quasianalyticity for Distributions and Ultradistributions
Publications of the Research Institute for Mathematical Sciences, 1995 openaire +3 more sources
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Siberian Mathematical Journal, 2012
The use of the ultradistribution semigroups is a main tool to analyze some pseudodifferential evolution systems having constant or nonconstant coefficients. In the present work, the authors study and analyze ultradistribution semigroups. They present the existence of fundamental solutions for Cauchy problems and analyze spectral characterizations of ...
Kostić, M., Pilipović, S.
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The use of the ultradistribution semigroups is a main tool to analyze some pseudodifferential evolution systems having constant or nonconstant coefficients. In the present work, the authors study and analyze ultradistribution semigroups. They present the existence of fundamental solutions for Cauchy problems and analyze spectral characterizations of ...
Kostić, M., Pilipović, S.
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Colombeau generalized ultradistributions
Mathematical Proceedings of the Cambridge Philosophical Society, 2001An algebra of Colombeau generalized ultradistributions in which the corresponding space of ultradistributions is embedded via regularizations and in which the multiplication of ultradifferentiable functions of an appropriate class is the ordinary multiplication is constructed.
Pilipović, S., Scarpalezos, D.
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Ultradistributional Wavelet Convolutors
Mathematical Methods in the Applied SciencesABSTRACTIn this paper, we explore wavelet convolutors in the ultradistribution space . We examine wavelet convolutors by applying an appropriate topological isomorphism to these spaces via the wavelet transform. Additionally, we present Calderóns reproducing formula for wavelet convolutors and provide an example using the Mexican hat wavelet transform
Abhishek Singh, Nikhila Raghuthaman
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Bilinear Hilbert Transform of Ultradistributions
Integral Transforms and Special Functions, 2002Following [1] we define the bilinear Hilbert transform of ultradistributions H_{\alpha}^{*} : {\cal D}^{\prime} (*, L^{2}) \times {\cal D} (*, L^{\infty}) \rightarrow {\cal D}^{\prime} (*, L^{2}) , respectively H_{\alpha}^{*}{:}\ {\cal D}^{\prime} (*, L^{q_{1}}) \times {\cal D} (*, L^{p_{2}}) \rightarrow {\cal D}^{\prime} (*, L^{q}) , where {\cal D ...
Buchkovska, Aneta L., Pilipović, Stevan
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Ultradistributions and Hyperbolicity
1977There are infinitely many classes of generalized functions, called ultradistributions, between the distributions of L. Schwartz [34] and the hyperfunctions of M. Sato [32]. Each class of ultradistributions have similar properties as the distributions or the hyperfunctions.
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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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