- #1
eljose
- 492
- 0
Let be the integral equation:
[tex]\int_{a}^{b}dyK(x,y)f(y)=g(x)[/tex]where f is unknown and g is known, then i use a resolvent Kernel in the form:
[tex]\int_{a}^{b}dyR(x,y)g(y)=f(x) [/tex] where we obtain the Kernel R by:
[tex]R=\sum_{n=0}^{\infty}b_{n}(K-I)^{n}[/tex] the last is Neumann series for the Kernel operator R..is my approach always true?..thanks.
[tex]\int_{a}^{b}dyK(x,y)f(y)=g(x)[/tex]where f is unknown and g is known, then i use a resolvent Kernel in the form:
[tex]\int_{a}^{b}dyR(x,y)g(y)=f(x) [/tex] where we obtain the Kernel R by:
[tex]R=\sum_{n=0}^{\infty}b_{n}(K-I)^{n}[/tex] the last is Neumann series for the Kernel operator R..is my approach always true?..thanks.