标题：The neutrix convolution product in
<mml:math alttext="$Z^\prime(m)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>Z</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and the exchange formula
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1998
卷号：21
DOI：10.1155/S0161171298000969
出版社：Hindawi Publishing Corporation
摘要：One of the problems in distribution theory is the lack of definition for convolutions and
products of distribution in general. In quantum theory and physics (see e.g. [1] and [2]), one finds that
some convolutions and products such as
1x⋅δ are in use. In [3], a definition for product of distributions
and some results of products are given using a specific delta sequence δn(x)=Cmnmρ(n2r2) in an
m-dimensional space. In this paper, we use the Fourier transform on D′(m) and the exchange formula to
define convolutions of ultradistributions in Z′(m) in terms of products of distributions in D′(m). We
prove a theorem which states that for arbitrary elements f˜
and g˜
in Z′(m), the neutrix convolution f˜⊗g˜ exists in Z′(m) if and only if the product f∘g
exists in D′(m). Some results of convolutions are
obtained by employing the neutrix calculus given by van der Corput [4].
