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Results tagged with approximation-theory
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user 169474
Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
1
vote
Accepted
Measurability of Brjuno numbers
I replace $\alpha$ by $x$ below.
Restricting ourselves to positive numbers is useless, since the property considered does not depend on $a_0(x) = \lfloor x \rfloor$. Therefore, $B$ is the union of all …
- 3,808
2
votes
Accepted
Smooth approximation of nonnegative, nondecreasing, concave functions
Replace the convolution on $\mathbb{R}$ by a convolution on the group $\mathbb{R}_+^*$, endowed with the invariant measure $dx/x$, namely set
$$f_n(x) := \int_0^\infty \varphi_n(y) f(x/y) \frac{dy}{y} …
- 3,808