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

Adem Kiliçman (2001)

Czechoslovak Mathematical Journal

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.

A Note on Multipliers for Integrable Boehmians

Nemzer, Dennis (2009)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 44A40, 42A38, 46F05The product of an entire function satisfying a growth condition at infinity and an integrable Boehmian is defined. Properties of this product are investigated.

A Tauberian theorem for distributions

Jiří Čížek, Jiří Jelínek (1996)

Commentationes Mathematicae Universitatis Carolinae

The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.

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