Defining compositions of \(x_+^\mu\), \(|x|^\mu\), \(x^{-s}\), and \(x^{-s}\ln |x|\) as neutrix limit of regular sequences

DOI10.1007/s40304-015-0076-8zbMath1359.46041OpenAlexW2226845867MaRDI QIDQ279692

Limonka Lazarova, Emin Özçağ, Biljana Tome Jolevska-Tuneska

Publication date: 29 April 2016

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40304-015-0076-8

zbMATH Keywords

Hadamard finite partregular sequencecomposition of distributionsdelta sequenceDirac delta functionneutrix calculuspseudo-function

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10)

Related Items (4)

Several results of fractional differential and integral equations in distribution ⋮ The composition of the distributions x−λlnsx− and x+−r/λ ⋮ On powers of the compositions involving Dirac-delta and infinitely differentiable functions ⋮ The convolution of analytic functionals

Cites Work

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• On defining the distributions \(\delta^k\) and \((\delta')^k\) by fractional derivatives
• On powers of the Heaviside function for negative integers
• Note on the distribution composition \((x_+^\mu )^\lambda \)
• On the neutrix composition of the distributionsx^−sln^m|x| andx^r
• A non-commutative neutrix product of distributions
• On the composition of the distributionsx⁻¹ln|x| and
• The theory of generalized functions
• Rules for integrals over products of distributions from coordinate independence of path integrals
• The distribution composition \((x_+^r)^{-s}\)

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