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On the composition of the distributions \(x^{-1} \ln|x|\) and \(x_+^r\). (English) Zbl 1105.46024

The authors give sense to and evaluate the distribution \((x_+^r)^{-1} \ln | x_+^r| \) for \(r=1,2,\dots\,\), following their papers [B. Fisher and K. Taş, Indian J.Pure Appl.Math.36, No. 1, 11–22 (2005; Zbl 1105.46023), reviewed above] and [B. Fisher and K. Taş, J. Math.Anal.Appl.318, No. 1, 102–111 (2006; Zbl 1105.46025), reviewed below] quite closely.

MSC:

46F10 Operations with distributions and generalized functions
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References:

[1] van der Corput J. G., Journal of Analyse Mathematique 7 pp 291– (1959)
[2] Fisher B., Rostocker Mathematisches Kolloquium 28 pp 75– (1985)
[3] Fisher B., Univerzitet u Novom Sadu Zbornik Radova Prirodno-Matematickog Fakulteta Serija za Matemati 15 pp 119– (1985)
[4] Gel’fand I. M., Generalized Functions (1964)
[5] Fisher B., Thai Journal of Mathematics 1 pp 39– (2003)
[6] DOI: 10.1080/10652460412331270661 · Zbl 1074.46025 · doi:10.1080/10652460412331270661
[7] Fisher B., Novi Sad Journal of Mathematics 32 pp 87– (2002)
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