Fredholm Alternative

In mathematics, the Fredholm alternative, named after Ivar Fredholm, is one of Fredholm's theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states that a non-zero complex number in the spectrum of a compact operator is an eigenvalue.

Read more about Fredholm Alternative:  Linear Algebra, Integral Equations, Functional Analysis

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Fredholm Alternative - Functional Analysis - Alternative
... In more precise terms, the Fredholm alternative only applies when K is a compact operator ... From Fredholm theory, smooth integral kernels are compact operators ... The Fredholm alternative may be restated in the following form a nonzero is either an eigenvalue of K, or it lies in the domain of the resolvent ...

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