Yi-Fan Wang

Toward P\'{o}lya's Conjecture: Improving the Individual Li-Yau Bound via Energy Orthogonality

We establish two complementary lower-bound mechanisms for individual eigenvalues of the Dirichlet Laplacian. First, energy orthogonality yields a frequency-dependent cap on the Fourier density of a finite spectral projection. Combining this cap with the standard $L^2$ Bessel estimate and a radial-capacity bathtub princ...