Results 11 to 20 of about 989 (103)
Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
International Journal of Mathematics and Mathematical Sciences, 2014 Let C be a regular cone in ℝ and let TC=ℝ+iC⊂ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of Lp-growth corresponding to TC.
Byung Keun Sohn
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Compatibility Conditions and the Convolution of Functions and Generalized Functions
Journal of Function Spaces and Applications, 2013 The paper is a review of certain existence theorems concerning the convolution of functions, distributions, and ultradistributions of Beurling type with supports satisfying suitable compatibility conditions.
Andrzej Kamiński +1 more
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Unified Treatment of the Krätzel Transformation for Generalized Functions
Abstract and Applied Analysis, 2013 We discuss a generalization of the Krätzel transforms on certain spaces of ultradistributions. We have proved that the Krätzel transform of an ultradifferentiable function is an ultradifferentiable function and satisfies its Parseval's inequality.
S. K. Q. Al-Omari, A. Kılıçman
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The neutrix convolution product in Z′(m) and the exchange formula
International Journal of Mathematics and Mathematical Sciences, 1998 One of the problems in distribution theory is the lack of definition for convolutions and products of distribution in general. In quantum theory and physics (see e.g.
C. K. Li, E. L. Koh
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Projective descriptions of spaces of functions and distributions
Mathematische Nachrichten, Volume 296, Issue 3, Page 915-937, March 2023., 2023 Abstract We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by seminorms, which are defined by a combination of classical norms and multiplication or convolution with certain functions.
Christian Bargetz +2 more
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On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces
International Journal of Differential Equations, Volume 2020, Issue 1, 2020., 2020 In the paper, we investigate a nonlocal multipoint by a time problem for the evolution equation with the operator A = (I − Δ)ω/2, Δ = (d2/dx2), and ω ∈ [1; −2) is a fixed parameter. The operator A is treated as a pseudodifferential operator in a certain space of type S. The solvability of this problem is proved.
V. V. Gorodetskiy +3 more
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Generalized Hermitean ultradistributions [PDF]
Mathematica Bohemica, 2009 Summary: We define, by duality methods, a space of ultradistributions \(\mathcal G _\omega ' (\mathbb R ^N)\). This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two.
Andrade, C., Loura, L.
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Analytic ultradistributions [PDF]
Proceedings of the American Mathematical Society, 1995 A necessary and sufficient condition that an ultradistribution, of Beurling or Roumieu type, which is defined on an open set Ω ⊂ R n \Omega \subset {\mathcal {R}^n} is a real analytic function is given.
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Karpatsʹkì Matematičnì Publìkacìï, 2013 The representation of convolution Gevrey algebra of ultradistributions as commutant of the $n$-parametric strongly continuous semigroup of shifts in algebra of linear and continuous mappings over the space of ultradifferentiable Gevrey functions with ...
A. V. Solomko
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On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution [PDF]
, 2017 We develop a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and use it as a base for the parametrix method in the study of new topological and structural properties ...
Pilipovic, Stevan +2 more
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