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Müntz's Theorem


Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed and bounded interval can be uniformly approximated by polynomials involving constants and any infinite sequence of powers whose reciprocals diverge.

In technical language, Müntz's theorem states that the Müntz space M(Lambda) is dense in C[0,1] iff

 sum_(i=1)^infty1/(lambda_i)=infty.

See also

Weierstrass Approximation Theorem

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References

Borwein, P. and Erdélyi, T. "Müntz's Theorem." §4.2 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, pp. 171-205, 1995.

Referenced on Wolfram|Alpha

Müntz's Theorem

Cite this as:

Weisstein, Eric W. "Müntz's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MuentzsTheorem.html

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