Tagged Questions
0
votes
1answer
58 views
Condition for the inverse laplace transform of a function to exist and bromwich integral
Given any function, is there any way of determining from the nature of the function, if it is the laplace transform of a piecewise continuous function of exponential order? For e.g. say the function ...
0
votes
1answer
23 views
Lambert transform of monomials
The Lambert transform of a function $f(x)$, is given by:
$$\int_{0}^{\infty}\frac{f(x)}{e^{xt}-1}dx\;\;\;\;(\Re(t)>0)$$
We wish for a closed form of the transform :
...
1
vote
1answer
77 views
arguing away - complex analysis
Probably a trivial question but I can't understand how to argue away the value of integrals in complex analysis.
I am trying to find the inverse Laplace transform of $F(s)=\frac{1}{s(s+1)}$. The ...
1
vote
0answers
27 views
Do integral transforms with meromorphic kernels always have analytic continuation?
Do integral transforms with meromorphic kernels always have analytic continuation ?
I think so, but I do not know how to prove it.
For clarity with analytic continuation I assume it was already ...
2
votes
1answer
60 views
Proof of the Direct mapping Theorem for Mellin transform.
I cannot understand an integration in the proof of the Direct mapping Theorem for the Mellin transform. A statement of the Theorem, together with an outline of the standard proof, can be found at page ...
1
vote
0answers
85 views
An integral transform.
Let's consider a complex function that can be represented in the following form:
$$
K(z)=\int_{-\infty}^{\infty}A(\alpha)z^\alpha d\alpha
$$
Writing $z=re^{i\theta}$, we get:
$$
...
1
vote
2answers
109 views
Z transform of a complex convolution
I found this paper on Hilbert Transform, which is a very nice read. I've studied signal processing, but from a more practical than mathematical perspective. Can someone explain to me how we arrive at ...
