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The purpose of this paper is to obtain a relation between thedistribution δ(2j)(r) and the operator △jδ and to give a sense to the convolution distributional productδ(2j)(r)∗δ(2s)(r) and the multiplicativedistributional products r−k⋅∇(△jδ) and (r−c)−k⋅∇(△jδ)

international journal of mathematics and mathematical sciences

A convolution product of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$(2j)$" id="E1"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>j</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>th derivative of Dirac's delta in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$r$" id="E2"><mml:mi>r</mml:mi></mml:math>and multiplicative distributional product between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" …

A convolution product of(2j)th derivative of Dirac's delta inrand multiplicative distributional product between