All Questions

The Euler--MacLaurin summation formula can be written as $$ \sum_{i=0}^{n-1} f(k)\approx \int^{n-1}_0f(x)\,dx + \frac{f(n-1) + f(0)}2 + \sum_{j=1}^m\frac{B_{2j}}{(2j)!}[f^{(2j - 1)}(n-1)...

Consider the standard mollifier $$ \phi(x) = C\exp\left(-\frac{1}{1-x^2}\right), \quad -1<x<1. $$ such that $\int\phi(x) = 1$. Let $f(x) = |x|$ and consider the convolution $f\ast \phi$. I am ...

tl;dr: Are there explicit bounds for the approximation error by orthogonal polynomials? There are various ways to formulate this question more precisely, so want I emphasize up front that this is a ...

Are there any bounds known for approximating a genuine multidimensional polynomial function with a sum one-dimensional polynomials over the independent variables? In the 2-dimensional case the ...

Have Feller semigroups been used to investigate the properties of the Cauchy problem associated with the fractional Laplacian (just like they have been used to study local degenerate second order ...