Find the eigenvalues and eigenfunctions of an integral operator

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Looking for eigenfunctions and eigenvalues of the integral operator



$$int _0^infty k(x, y) phi (x) dx$$, with



$$K(x, y) = exp left[ -beta left(fracnu4 (x^2 + y^2) + fracmu2 (x + y) right) right].$$
I have no solid basis on this subject, so I don't know how to start.










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  • Look up "Mehler's formula".
    – kimchi lover
    Sep 4 at 11:12














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Looking for eigenfunctions and eigenvalues of the integral operator



$$int _0^infty k(x, y) phi (x) dx$$, with



$$K(x, y) = exp left[ -beta left(fracnu4 (x^2 + y^2) + fracmu2 (x + y) right) right].$$
I have no solid basis on this subject, so I don't know how to start.










share|cite|improve this question





















  • Look up "Mehler's formula".
    – kimchi lover
    Sep 4 at 11:12












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Looking for eigenfunctions and eigenvalues of the integral operator



$$int _0^infty k(x, y) phi (x) dx$$, with



$$K(x, y) = exp left[ -beta left(fracnu4 (x^2 + y^2) + fracmu2 (x + y) right) right].$$
I have no solid basis on this subject, so I don't know how to start.










share|cite|improve this question













Looking for eigenfunctions and eigenvalues of the integral operator



$$int _0^infty k(x, y) phi (x) dx$$, with



$$K(x, y) = exp left[ -beta left(fracnu4 (x^2 + y^2) + fracmu2 (x + y) right) right].$$
I have no solid basis on this subject, so I don't know how to start.







integration functional-analysis






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asked Sep 4 at 11:08









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  • Look up "Mehler's formula".
    – kimchi lover
    Sep 4 at 11:12
















  • Look up "Mehler's formula".
    – kimchi lover
    Sep 4 at 11:12















Look up "Mehler's formula".
– kimchi lover
Sep 4 at 11:12




Look up "Mehler's formula".
– kimchi lover
Sep 4 at 11:12















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