On the Composition and Neutrix Composition of the Delta Function with the Hyperbolic Tangent and Its Inverse Functions
نویسندگان
چکیده
منابع مشابه
On the Composition and Neutrix Composition of the Delta Function with the Hyperbolic Tangent and Its Inverse Functions
Let F be a distribution in D′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ rs−1 tanhx 1/r ...
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A Result on the Neutrix Composition of the Delta Function
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 compo...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2011
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2011/846736