Müntz,s Theorem
المؤلف:
Borwein, P. and Erdélyi, T.
المصدر:
"Müntz,s Theorem." §4.2 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag
الجزء والصفحة:
pp. 171-205
17-11-2021
1674
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 
is dense in ![C[0,1]](https://mathworld.wolfram.com/images/equations/MuentzsTheorem/Inline2.gif)
iff
REFERENCES:
Borwein, P. and Erdélyi, T. "Müntz's Theorem." §4.2 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, pp. 171-205, 1995.
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