Results 11 to 20 of about 370 (125)
Tempered Boehmians and ultradistributions [PDF]
Proceedings of the American Mathematical Society, 1995 An extension of the Fourier transform which is a one-to-one continuous mapping from the space of tempered Boehmians onto the space of Schwartz distributions is introduced. This shows that the space of tempered Boehmians can be identified with the space
Mikusiński, Piotr, Piotr Mikusiński
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Structural theorems for periodic ultradistributions [PDF]
Proceedings of the American Mathematical Society, 1986 Structural theorems for periodic ultradistributions of Roumieu and Beurling types are given.
Stevan Pilipović
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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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Rotation Invariant Ultradistributions [PDF]
, 2017 We prove that an ultradistribution is rotation invariant if and only if it coincides with its spherical mean. For it, we study the problem of spherical representations of ultradistributions on $\mathbb{R}^{n}$. Our results apply to both the quasianalytic and the non-quasianalytic case.
Vuckovic, Dorde, Vindas Diaz, Jasson
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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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Equivalence of the defining sequences for ultradistributions [PDF]
Proceedings of the American Mathematical Society, 1993 We prove that M p ∗
Chung, Soon-Yeong, Kim, Dohan
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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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Operator representation of Gevrey ultradistributions algebra with supports on positive $n$-dimensional angle [PDF]
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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Bochner–Schwartz Theorems for Ultradistributions [PDF]
Journal of Mathematical Analysis and Applications, 1998 Das Bochner Theorem für eine positiv definite, stetige Funktion \(f\) in \(\mathbb{R}^n\) sagt aus, dass die folgenden drei Bedingungen äquivalent sind: (1) \(f\) ist positiv definit, (2) \(f\) ist die Fourier Transformatierte eines positiven, endlichen Maßes, (3) für jede \(C^\infty\) Funktion \(\varphi\) mit kompaktem Träger gilt \[ \iint \overline{f(
Cho, Jonggyu +2 more
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