eljose
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let be the integral equation:
[tex]f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y)[/tex]
where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:
[tex]f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y)[/tex]
My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...
[tex]R= \sum_{n=0}^{\infty} \lambda ^ n K^{n}[/tex]
for K^n the n-th iterated kernel since the equation is HOmogeneus (all the functions involved except the Kernel are unknown) or if we have enough with the iteration procedure to solve the equation..thanks.
[tex]f(x)=\lambda \int_{0}^{1}dyK(x,y)f(y)[/tex]
where the Kernel is known and "lambada" is an small eigenvalue... the question is if i want to solve i propose the iterative scheme:
[tex]f_{n+1} (x)=\lambda \int_{0}^{1}dyK(x,y)f_n(y)[/tex]
My question is if in this case i can propose a "Neumann series" for the resolvent Kernel R(x,y) in the form...
[tex]R= \sum_{n=0}^{\infty} \lambda ^ n K^{n}[/tex]
for K^n the n-th iterated kernel since the equation is HOmogeneus (all the functions involved except the Kernel are unknown) or if we have enough with the iteration procedure to solve the equation..thanks.
