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On some neutrix products of distributions. (English) Zbl 0734.46028

A more general product of distributions, called neutrix product of distributions, has been introduced by the first author [Math. Nachr. 108, 117-127 (1982; Zbl 0522.46025)]. This paper has analysed and explicitly calculated several neutrix products involving slowly varying functions. More specifically, neutrix product of the distributions \(x^{\lambda}_+L(x)\) and \(x^{\mu}\) or \(\delta^{(m)}\) has been analysed and explicitly calculated where \(\lambda\),\(\mu\not\in Z\), \(m\in N_ 0\) and L is a slowly varying function at both zero and infinity [E. Seneta, Regularly varying functions, Lect. Notes Math. 508 (1976; Zbl 0324.26002)].

MSC:

46F10 Operations with distributions and generalized functions
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