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Pseudo differential operators

  1. Jul 31, 2007 #1
    let be the operator involving an infinite-dimensional ODE

    [tex] f( \partial _{x}) y(x)=h(x) [/tex]

    then if h(x)=0 i make the ansatz [tex] y(x)=e^{ax} [/tex] so

    [tex] \sum_{\rho } e^{x\rho} [/tex] [tex] f(\rho) =0 [/tex]

    for h(x) different from '0' we construct an orthonormal basis with the solutions given above to give an expression on the interval (0,c)

    Another question,.. can we give a 'meaning' to the expression.

    [tex] G(x,y)= \int dV \frac{e^{ik|x-y|}{E-Ak^{2}-V(\partial _{k})} [/tex]
  2. jcsd
  3. Jul 31, 2007 #2
    i meant the operator

    [tex] \int_{a}^{b}dx \frac{exp(-iux)}{x+f(\partial)-5} [/tex]

    where the derivative is respect to 'x'
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