Existence of Solutions
One of the Fredholm theorem's closely related to the Fredholm alternative, concerns the existence of solutions to the inhomogeneous Fredholm equation
Solutions to this equation exist if and only if the function is orthogonal to the complete set of solutions of the corresponding homogeneous adjoint equation:
where is the complex conjugate of and the former is one of the complete set of solutions to
A sufficient condition for this theorem to hold is for to be square integrable on the rectangle .
Read more about this topic: Fredholm's Theorem
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