Yakun Xi

activity

20242026

collaborators

6 papers

math.SP2026

Kuznecov formulas for domains with fractal boundary

Xucheng Hu, Yakun Xi

Let $(M, g)$ be a compact $d$ -dimensional Riemannian manifold without boundary, and let ${e_{j}}_{j = 0}^{\infty}$ be an orthonormal basis of Laplace eigenfunctions with frequencies $\{…

math.AP2026

Polygons and multi-product of eigenfunctions

Emmett L. Wyman, Yakun Xi, Yi Zhang

Let $M$ be a compact Riemannian manifold without boundary, with $L^{2}$ -normalized Laplace-Beltrami eigenfunctions ${e_{j}}_{j}$ , which satisfy $Δ_{g} e_{j} = - λ_{j}^{2} e_{j}$ . We study the fol…

math.AP2026

Kuznecov formulae for fractal measures

Yakun Xi

Let $(M, g)$ be a compact, connected Riemannian manifold of dimension $n \geq 2$ , and let ${e_{j}}_{j = 0}^{\infty}$ be an orthonormal basis of Laplace eigenfunctions $- Δ_{g} e_{j} = λ_{j}^{2} e_{j}$ …

math.AP2025

Kuznecov remainders and generic metrics

Vadim Kaloshin, Emmett L. Wyman, Yakun Xi

We obtain improved remainder estimates in the Kuznecov sum formula for period integrals of Laplace eigenfunctions on a Riemannian manifold $M$ . Building upon the two-term asymptoti…

math.AP2024

Hearing the shape of a drum by knocking around

Xing Wang, Emmett L. Wyman, Yakun Xi

We study a variation of Kac's question, "Can one hear the shape of a drum?" if we allow ourselves access to some additional information. In particular, we allow ourselves to ``hear…

math.CO2024

Cospectral vertices, walk-regular planar graphs and the echolocation problem

Shi-Lei Kong, Emmett L. Wyman, Yakun Xi

We study cospectral vertices on finite graphs in relation to the echolocation problem on Riemannian manifolds. First, We prove a computationally simple criterion to determine wheth…