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MathGroup Archive 2003

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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


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