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Let $g(x)\colon [-2,2]\to \mathbb{R}$ be a continuous function. Let $f_n(x)$ be a polynomial of degree $n$ such that $\log |f_n(x)|\leqslant ng(x)$ for all $x\in [-2,2]$. Then the maximal possible ...

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)...

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 ...