*** y(t) is Z(s) = X(s) . Y(s).**

In the demonstration of this, I fail to see why we are allowed to

separate a double integral in two independent integrals.

z(t) = x(t) *y(t) = Integral from -inf to +inf [x(u) . y(t-u) du]

In the demonstration of this, I fail to see why we are allowed to

separate a double integral in two independent integrals.

z(t) = x(t) *

Now let us calculate the two-sided(? - the one that goes from -inf to

+inf) Laplace Transform. It is called «bilatère» in French. What is

the correct English adjective?

Z(s) = Integ from -inf to +inf{Integ from -inf to +inf

[x(u).y(t-u).du] . exp(-s.t).dt}

I move the closing bracket to the end

= Integ from -inf to +inf{Integ from -inf to +inf [x(u).y(t-u).du

. exp(-s.t).dt]}

I add two exponentials which have 1 as a product

= Integ from -inf to +inf{Integ from -inf to +inf

[x(u).exp(-u.t).y(t-u).du.exp(-s.t).exp(u.t) dt]}

Now, I simplify a bit and I move «du» to the left

= Integ from -inf to +inf{Integ from -inf to +inf

[x(u).exp(-u.t).y(t-u).du . exp[-s(t-u)].dt]}

= Integ from -inf to +inf{Integ from -inf to +inf

[x(u).exp(-u.t).du . y(t-u).exp[-s(t-u)].dt]}

On the left side, we see an integral with respect to u variable.

On the right side, if we are allowed to make dt = d(t-u), we can

substitute v for t-u, and we can separate the integrals.

Why are we allowed to make dt = d(t-u)? This assumes that u is a

constant while u sweeps from -inf to +inf!

This message does not deal with an engineering problem but with a

maths problem. Could you suggest a more suitable newsgroup?

Writing this message without the usual mathetical notation was

difficult. Reading it is difficult. Is there a software tool that

permits a better rendering of mathematical expressions with only the

ASCII character set?

Thank you very much for your enlightenment.