0
votes
2answers
25 views

Fourier Transform-1

I am trying to solve a Fourier transform problem and I am stuck. The problem is: $$f(t)= \frac{\sin(2t)}{e^{|t|}}.$$ I have used integration, but the answer that I come up with is different than ...
0
votes
0answers
15 views

Solution to recursion relation using Mellin transform

I have been trying to solve the following recursive equation for $0<x_c<1$ for few a days: $$ P(x) = 2\mathbf{1}_{0\leq x\leq x_c} + 2\int_x^1 dy P\left(\frac{x}{y}\right)y^{-1} ...
0
votes
2answers
56 views

Laplace transform of $L({1-e^{-t}\over t})$

I have to find the Laplace transform of $$\mathcal{L}\left[\dfrac{1-e^{-t}}t\right],$$ then this is equivalent to $$\mathcal{L}\left[\dfrac{1}t\right]-\mathcal{L}\left[\dfrac{e^{-t}}t\right]$$ But ...
0
votes
1answer
124 views

A problem about Laplace transform and Parseval–Plancherel theorem

I am reading a paper about fractional differential equation. One of the piece said as follow: By applying the Parseval–Plancherel theorem we may show: \begin{equation} \int_0^\infty ...
1
vote
0answers
23 views

Conditions on $F(y)$ for the existence of $f(x)$ where $F(y) = \int_{0}^{\infty} y \exp{[(-\frac{1}{2}(y^2 + x^2)]} I_{0}(xy) f(x) \; \mathrm{d}x$

I've been working with the following integral transform: $$F(y) = \int_{0}^{\infty} y \exp{\left[-\frac{1}{2}(y^2 + x^2)\right]} I_{0}(xy) f(x) \; \mathrm{d}x$$ where: $x,y$ are positive-definite ...
1
vote
1answer
80 views

Change of variables in double integral - what's wrong?

I have a homework problem, as follows: Evaluate the double integral by making an appropriate change of variables. $\iint_R 9\sin(49x^2+16y^2)\,dA$, where $R$ is the region in the first ...
1
vote
1answer
91 views

How to find the inverse mellin transform?

On the wikipedia page http://en.wikipedia.org/wiki/Mellin_transform the second formula is an integral transformation for the inverse Mellin transform. Being new to integral transforms, I wonder how ...
1
vote
2answers
105 views

Laplace Transformation Applications

In one of our Mathematics lecture our Prof told us that similar to Logarithmic Transformations we can use Laplace Transformations to solve difficult equations. What kind of equations do Laplace ...
2
votes
0answers
86 views

Continuity of the inverse Laplace Transform

If I know $Y(s)$, can I predict when $\mathscr{L}^{-1}[Y(s)]=y(t)$ will be continuous or continuously differentiable or even stronger conditions? For example; I'm solving an ODE with the Laplace ...
1
vote
0answers
164 views

Inverting an integral transform

This question is either very obvious or by nature unsolvable in a general case. I Google'd around for a solution to no avail. Given an integral transform of kernel K across some interval I as a ...
1
vote
1answer
188 views

About mellin convolution technique

Recently I was studying the mellin convolution technique to solve definite integrals. I am just wondering is the technique valid only for any definite integrals (with any range $\int^b_a$)? or only ...