Research Information System
Integral Transforms and Special Functions, vol.4, no.1-2, pp.77-82, 1996 (Scopus)
Let f and g be distributions in script D sign′ and let fn(x) = f(x)κn(x), gn(x) = g(x)κn(x), where κn(x) is a certain function which converges to the identity function as n tends to infinity. Then the commutative neutrix convolution product f △ g is defined as the neutrix limit of the sequence {fn * gn}, provided the limit h exists in the sense that N-limn→∞〈fn * gn, ∅〉 = 〈h, ∅〉 for all ∅ ∈ script D sign. If now δn(σ) = (2π)±1ℱ(κn), where ℱ denotes the Fourier transform, then the neutrix product f̄△ḡ is defined by equation f̄△ḡ = ℱ(f △ g). Some results are given.