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On the space of ultradistributions vanishing at infinity [PDF]

Banach Journal of Mathematical Analysis, 2020
We study the structural and linear topological properties of the space (omega)'* of ultradistributions vanishing at infinity (with respect to a weight function omega).
Andreas Debrouwere, Lenny Neyt, Jasson Vindas   +2 more
exaly   +3 more sources

Almost subadditive weight functions form Braun–Meise–Taylor theory of ultradistributions [PDF]

Journal of Mathematical Analysis and Applications, 2010
As it is known, Roumieu–Komatsu theory of ultradistributions is strictly larger than Beurling–Björck one and that the latter theory is established by the class of all subadditive weight functions.
Alexander V Abanin, Pham Trong Tien
exaly   +2 more sources

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Ultradistribution semigroups

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.
openaire   +1 more source

Ultradistributional Wavelet Convolutors

Mathematical Methods in the Applied Sciences
ABSTRACTIn 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, 2002
Following [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

1977
There 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.
openaire   +1 more source

Colombeau generalized ultradistributions

Mathematical Proceedings of the Cambridge Philosophical Society, 2001
An 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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On hankel transforms of ultradistributions

Applicable Analysis, 1985
On developpe une theorie des espaces de fonctions test Hμ ,ad k, Hμ bq et Hμ ,ad k bq . Ce sont des generalisations des espaces fonctions test de type Hμ. Les elements des espaces duaux sont appeles ultradistributions. On montre que la transformation de Hankel hμ pour μ≥-1/2 est une application lineaire continue pour chacun de ces espaces dans ...
R. S. Pathak, A. B. Pandey
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On the convolution in the space of Beurling ultradistributions

Commentarii Mathematici Universitatis Sancti Pauli, 1991
The author establishes two definitions of convolution in the space of Beurling ultradistributions \({\mathcal D}^{'(M_ p)}\) by following the procedure of Schwartz and Vladimirov, separately, for the convolution of distributions. He proves that: (1) The two given definitions are equivalent; (2) If \(f\) and \(g\) belong to \({\mathcal D}^{'(M_ p ...
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Oscillatory Integrals As Ultradistributions

Integral Transforms and Special Functions, 2001
An oscillatory integral of the form naturally defines a distribution provided that φ is a phase function and a is a symbol in Hormander's symbol class. In this paper extending this result to the case of Gevrey class we show that the above oscillatory integral defines a Gevrey ultradistribution provided that φ is a Gevrey phase function and a is a ...
Nam-Gyu Kang, Soon-Yeong Chung, Dohan Kim   +2 more
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