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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 $N^{-α_p}$ with a
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