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The definition of the two-sided Laplace transform is
Under the substitution , this transforms into
So the relationship between Mellin transform and two-sided Laplace transform should be
rather than the stated
-- 212.18.24.11 14:58, 22 August 2005 (UTC)
Hello my question is ..let's suppose we know the Mellin inverse transform of F(s) then..how could we calculate the Mellin inverse transform of F(as) when a is a real number, i believe that if g(x) has F(s) as its Mellin transform then is the inverse of F(as) but i'm not pretty sure -- Karl-H 14:20, 1 October 2006 (UTC)
Hello, I have a question -- the example transform of the function
is apparently not convergent on the positive real line since the integral of diverges - but you state that the function must be integrable on the positive real line to have a Mellin transform? Could you correct this apparent inconsistency or explain the condition for having a Mellin transform a bit more clearly? -- 81.146.66.114 14:38, 24 March 2007 (UTC)
I think this article could use some restructuring.
Your thoughts?
-- Joe056 02:19, 15 March 2007 (UTC)
I think there's a mistake here. The article says
First of all, I presume that what is intended is The magnitude of the Mellin Transform of a scaled function is identical to the magnitude of the Mellin Transform of the original function. But I don't think even this is correct. Just as the shift invariance of the magnitude of the Fourier transform does not hold for the Laplace transform, the scale invariance property as stated here does not hold for the Mellin transform (though I suspect it holds for purely imaginary z). Consider for examle, the Mellin transform of exp(-at), as given here [1]. 72.75.103.224 03:24, 2 July 2007 (UTC)
The article indicates the following:
The two-sided Laplace transform may be defined in terms of the Mellin transform by
and conversely we can get the Mellin transform from the two-sided Laplace transform by
This seems inconsistent with the following link which indicates the subsequent text: Laplace Transform
The Mellin transform and its inverse are related to the two-sided Laplace transform by a simple change of variables.
If in the Mellin transform
we set θ = e−t we get a two-sided Laplace transform.
This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
The definition of the two-sided Laplace transform is
Under the substitution , this transforms into
So the relationship between Mellin transform and two-sided Laplace transform should be
rather than the stated
-- 212.18.24.11 14:58, 22 August 2005 (UTC)
Hello my question is ..let's suppose we know the Mellin inverse transform of F(s) then..how could we calculate the Mellin inverse transform of F(as) when a is a real number, i believe that if g(x) has F(s) as its Mellin transform then is the inverse of F(as) but i'm not pretty sure -- Karl-H 14:20, 1 October 2006 (UTC)
Hello, I have a question -- the example transform of the function
is apparently not convergent on the positive real line since the integral of diverges - but you state that the function must be integrable on the positive real line to have a Mellin transform? Could you correct this apparent inconsistency or explain the condition for having a Mellin transform a bit more clearly? -- 81.146.66.114 14:38, 24 March 2007 (UTC)
I think this article could use some restructuring.
Your thoughts?
-- Joe056 02:19, 15 March 2007 (UTC)
I think there's a mistake here. The article says
First of all, I presume that what is intended is The magnitude of the Mellin Transform of a scaled function is identical to the magnitude of the Mellin Transform of the original function. But I don't think even this is correct. Just as the shift invariance of the magnitude of the Fourier transform does not hold for the Laplace transform, the scale invariance property as stated here does not hold for the Mellin transform (though I suspect it holds for purely imaginary z). Consider for examle, the Mellin transform of exp(-at), as given here [1]. 72.75.103.224 03:24, 2 July 2007 (UTC)
The article indicates the following:
The two-sided Laplace transform may be defined in terms of the Mellin transform by
and conversely we can get the Mellin transform from the two-sided Laplace transform by
This seems inconsistent with the following link which indicates the subsequent text: Laplace Transform
The Mellin transform and its inverse are related to the two-sided Laplace transform by a simple change of variables.
If in the Mellin transform
we set θ = e−t we get a two-sided Laplace transform.