Math
show the completeness of the space of generalized functions?
Asked by
dream19
Last updated by
anonymous
A set of orthogonal functions is termed complete in the closed interval if, for every piecewise continuous function in the interval, the minimum square error
(where denotes the L2-norm with respect to a weighting function ) converges to zero as becomes infinite. Symbolically, a set of functions is complete if
![lim_(m->infty)int_a^b[f(x)-sum_(n=0)^ma_nphi_n(x)]^2w(x)dx=0,](http://mathworld.wolfram.com/images/equations/CompleteOrthogonalSystem/NumberedEquation2.gif)
where the above integral is a Lebesgue integral.
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