Displaying similar documents to “On the incomplete gamma function and the neutrix convolution”

A comparison on the commutative neutrix convolution of distributions and the exchange formula

Adem Kiliçman (2001)

Czechoslovak Mathematical Journal

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Let f ˜ , g ˜ be ultradistributions in 𝒵 ' and let f ˜ n = f ˜ * δ n and g ˜ n = g ˜ * σ n where { δ n } is a sequence in 𝒵 which converges to the Dirac-delta function δ . Then the neutrix product f ˜ ⋄ g ˜ is defined on the space of ultradistributions 𝒵 ' as the neutrix limit of the sequence { 1 2 ( f ˜ n g ˜ + f ˜ g ˜ n ) } provided the limit h ˜ exist in the sense that N - l i m n → ∞ 1 2 〈 f ˜ n g ˜ + f ˜ g ˜ n , ψ 〉 = 〈 h ˜ , ψ 〉 for all ψ in 𝒵 . We also prove that the neutrix convolution product f ♦ * g exist in 𝒟 ' , if and only if the neutrix product f ˜ ⋄ g ˜ exist in 𝒵 ' and the exchange formula F ( f ♦ * g ) = f ˜ ⋄ g ˜ is then satisfied.