The Fredholm Alternative is a principle in functional analysis that provides conditions under which a linear operator equation has solutions. It essentially states that for a compact linear operator on a Banach space, either the equation has a unique solution, or it has infinitely many solutions, depending on the properties of the operator and the right-hand side of the equation. This concept is particularly important when dealing with compact operators on Banach spaces, linking the existence of solutions to the kernel and range of these operators.
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