A Result on the Neutrix Composition of the Delta Function
نویسندگان
چکیده
The neutrix composition F (f(x))) of a distribution F (x) and a locally summable function f(x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x) = F (x) ∗ δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). It is proved that the neutrix composition δ(rsm−pm−1)(x + /(1 + x 1/m + )) exists for r, s,m = 1, 2, 3 . . . and p = 0, 1, 2, . . . , rs− 1. AMS Subject Classifications: 46F10.
منابع مشابه
On the Composition and Neutrix Composition of the Delta Function with the Hyperbolic Tangent and Its Inverse Functions
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