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## Main Question or Discussion Point

Hi all.

I'm currently working on a problem that has led me to an integral equation of the form:

[tex] u(t)=\int_0^t K(t,\tau)f(\tau)\, \mathrm{d}\tau \qquad t\in (0,T)[/tex]

or simply [tex]u=Kf[/tex]. I've managed to prove the following:

Does anyone know of any references that deal with this stuff (journal access isn't a problem)?

I'm currently working on a problem that has led me to an integral equation of the form:

[tex] u(t)=\int_0^t K(t,\tau)f(\tau)\, \mathrm{d}\tau \qquad t\in (0,T)[/tex]

or simply [tex]u=Kf[/tex]. I've managed to prove the following:

- [tex]K :L^2(0,T)\rightarrow L^2 (0,T)[/tex]
- [tex]K[/tex] is compact.
- [tex]u\in L^2(0,T)[/tex]
- The kernel [tex]K(t,\tau)[/tex] has a weak singularity.

Does anyone know of any references that deal with this stuff (journal access isn't a problem)?