The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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.