On Some Spaces of Distributions

Adina Chirilă (), Marin Marin and Andreas Öchsner
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Adina Chirilă: Transilvania University of Braşov, Department of Mathematics and Computer Sciences
Marin Marin: Transilvania University of Braşov, Department of Mathematics and Computer Sciences
Andreas Öchsner: Esslingen University of Applied Sciences, Faculty of Mechanical Engineering

Chapter Chapter 11 in Distribution Theory Applied to Differential Equations, 2021, pp 249-262 from Springer

Abstract: Abstract We present the spaces $$\mathcal {D}_{L^p}$$ D L p and their properties. We also present their duals and their properties. Then we ask which is the most general space of distributions operating continuously on $$\mathcal {S}'$$ S ′ by convolution and such that the Fourier transform maps convolution products into the product of the corresponding Fourier transforms. So we present the space $$\mathcal {O}'_C$$ O C ′ and its properties.

Date: 2021
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DOI: 10.1007/978-3-030-67159-4_11

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