Yuri Malykhin

Low-dimensional approximation of uniformly bounded orthonormal systems

We prove that if $f_1,\ldots,f_N$ is an uniformly bounded orthonormal system, then for all $p\in[1,2)$ there is an estimate for its Kolmogorov widths: $d_n(\{f_1,\dots,f_N\},L_p) \gtrsim \min\{1,n^{-1/p}N^{1/2}\}$, $n\le N/2$. In the regime $n\asymp N$ this provides the lower bound $N^{-\alpha_p}$ with a sharp exponent...