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Toward Pólya'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-ca
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