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Some results on the non-commutative neutrix product of distributions. (English) Zbl 1171.46031

Summary: It is proved that the non-commutative neutrix product of the distributions \(x^{-r}\) and \(x^s \ln ^q|x|\) exists and \[ x^{-r}\circ (x^s \ln^q |x|)=x^{-r+s}\ln^{q}|x| \] for \(r,q=1,2,\dots\), \(s=0,\pm 1,\pm 2,\dots\), \(r-s>1\).

MSC:

46F10 Operations with distributions and generalized functions
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[1] DOI: 10.1093/qmath/22.2.291 · Zbl 0213.13104 · doi:10.1093/qmath/22.2.291
[2] DOI: 10.1002/mana.19800990126 · Zbl 0468.46027 · doi:10.1002/mana.19800990126
[3] DOI: 10.1002/mana.19821080110 · Zbl 0522.46025 · doi:10.1002/mana.19821080110
[4] DOI: 10.1080/1065246042000272018 · Zbl 1075.46035 · doi:10.1080/1065246042000272018
[5] Fisher B., Rad. Mat. 10 pp 85– (2000)
[6] Gel’fand, I. M. and Shilov, G. E. 1964. ”Generalized Functions”. Vol. I, New York: Academic Press.
[7] van der Corput J. G., J. Anal. Math. 7 pp 291– (1959)
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