Author

Hao-Nan Wu

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Preprint Sep 2026

Positivity loss in bandlimited spectral reproduction on spheres

How small can the positivity loss be for an $N$-bandlimited spectral operator that exactly reproduces all modes up to degree $L$? For spherical polynomial approximation on $\mathbb S^d$, we prove that the smallest possible excess of the uniform operator norm above 1, equivalently the least positivity loss, is of sharp...

Hao-Nan Wu · 0 citations

Preprint Aug 2026

Nearly tight framelet systems from nested Marcinkiewicz--Zygmund measures on compact Riemannian manifolds

Tight framelet systems on manifolds provide exact energy preservation and one-pass reconstruction, but their standard semi-discretization relies on polynomial-exact quadrature rules, which are difficult to reconcile with scattered and progressively refined data. We develop nested Marcinkiewicz--Zygmund (MZ) measures on...

Hao-Nan Wu, Xiaosheng Zhuang · 1 citation