Re: Defining Operators
- To: mathgroup at smc.vnet.net
- Subject: [mg44803] Re: Defining Operators
- From: Roberto Brambilla <rlbrambilla at cesi.it>
- Date: Thu, 27 Nov 2003 11:38:29 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hi Guthery, try this
IntegrationOperator[f_,s_]:= Module[{func},
func=Function@@{f /.s -> #1};
Integrate[func[s],{s,0,1}]
where s is the integration variable, that, of course, must be present in
the arguments of the function to be integrate.
Example
g[x_,y_,z_]:=x Cos[w y] Tanh[m z]
f[[t_,y_]:=Evaluate[IntegrationOperator[g[x,t,y],x]
h[x_,q_]:=Evaluate[IntegrationOperator[g[x,t,q],t]
r[x1_,x2_]:=Evaluate[IntegrationOperator[g[x1,x2,s],s]
?f
f[t_,y_]:=1/2 Cos[w t] Tanh[m y]
?h
h[x_]:= x Sin[w]Tanh[mq]/w
?t
r[x1_,x2_]:=x1 Cos[w x2]Log[Cosh[m]]/m
You can also add a kernel to integrals , as in integral transforms
Kern[x_,y_]:= Exp[ - x y]
myTransform[f_,x_,p_]:= Module[{func},
func=Function@@{f /.x-> #1};
Integrate[func[x]Kern[x,p],{x,0,Infinity},GenerateConditions->False]]
Example:
myTransform[BesselJ[0,w y],y,z]
1/Sqrt[w^2+z^2]
Bye Rob
Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.02.2125.5875
fax +39.02.2125.5492
rlbrambilla at cesi.it