An existence theorem for the commutative neutrix product of distributions (Q2714214)
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scientific article; zbMATH DE number 1604045
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence theorem for the commutative neutrix product of distributions |
scientific article; zbMATH DE number 1604045 |
Statements
12 June 2001
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distribution
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delta-function
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neutrix limit
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neutrix product
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0.9511542
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0.9483316
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0.9440061
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0.9376166
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An existence theorem for the commutative neutrix product of distributions (English)
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A definition of the distribution \(x_+^{-r}\) is given in order that it satisfies the equation \((x^{-r}_+)'=-rx^{-r-1}_+.\) NEWLINENEWLINENEWLINEThe existence of the neutrix-products \(x^{-r}_+\) \(\ln x_+\) is proved for \(r,s=1,2,\dots\). NEWLINENEWLINENEWLINEAs a particular case it follows that the usual product \(x^{-1} \cdot\ln x_+\) exists and it represents the distribution \(x^{-1}_+\ln x_+\) defined as being the derivative of \(\frac{1}{2}\ln^2x_+.\)
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