       integral tranform definition

• To: mathgroup at smc.vnet.net
• Subject: [mg33130] integral tranform definition
• From: Roberto Brambilla <rlbrambilla at cesi.it>
• Date: Tue, 5 Mar 2002 03:08:31 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi all math-friends,

I have a little problem in integral transform definition.
I want to define the following integral transform depending on a parameter n

g(y,n)=integral[K(n,y,x)f(x)dx] (a<=x<=b)

where, for example, Kern(n,y,x)=sin(n x y)  in (0-2Pi) square.

So a I build the function

MyTransf[n_, func_, y_] :=  Integrate[Kern[n, y, x] func[x],
{x, 0, 2 Pi}] // FullSimplify

and try it

test1[x_]:=Cos[5 x]
g[t_, m_] := Evaluate[MyTransf[m, test1, t]]

m=4; g[z,m]
(out)  8 z (Sin[4 pi z])^2/(16 z2-25)

So far so good. Now I want to apply MyTransf again to this result, changing
the parameter.
I have to define an intermediate function without parameters and sigle
variable

test2[x_]:=g[x,4]

and then

m=2;
Evaluate[MyTransf[m, test2, t]]
(out) 1/16((-CosIntegral[.................etc.........

My problem is to avoid the definition of the intermediate function.
How can define MyTrans so that I can write simply

MyTransf[n, func[m1,m2,...,x], y]

i.e a definition where I can use funcions with explicited parameter(s)
m1,m2..,
the name of the input variable (here x) and the name of the output variable
(here y)?
Having this definition, I could write (my final wish)

MyTransf[n2, MyTransf[n1, f1[m1,x], y], z]

and then find for each n1 the vale of n2 (if exist) for which this double
transform
correspond to other transform, i.e. I want to test if these transforms act
like a group.
Rob.

Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.02.2125.5875
fax +39.02.2125.5492
rlbrambilla at cesi.it

```

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