Xinyuan Xie

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20242026

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math.FA2026

The König constant is one

Xinyuan Xie, Haonan Zhang

For each $N \geq 1$ , consider the normalized König bilinear form $B_{K} : L_{\infty} (R^{N}) \times L_{\infty} (R^{N}) \to R$ given by \[ B_{\mathrm K}(f,g):=\frac{1…

math.FA2024

Jackson's inequality on the hypercube

Paata Ivanisvili, Roman Vershynin, Xinyuan Xie

We investigate the best constant $J (n, d)$ such that Jackson's inequality \[ \inf_{\mathrm{deg}(g) \leq d} \|f - g\|_{\infty} \leq J(n,d) \, s(f), \] holds for all functions $f$ on…