A set of functions is termed a complete biorthogonal system in the closed interval if, they are biorthogonal, i.e.,
(1)
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(2)
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(3)
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(4)
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(5)
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and complete.
A complete biorthogonal system has a very special type of generalized Fourier series. The prototypical example of a complete biorthogonal system is over , which can be used as a basis for constructing "the" Fourier series of an arbitrary function.