Proves a generalised eigenvector expansion for infinite Toeplitz matrices with completely monotone entries, giving real eigenvalues and eigenvectors even when the matrix is not normal.
On the curvature of level sets of harmonic functions
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abstract
If a real harmonic function inside the open unit disk $B(0,1) \subset \mathbb{R}^2$ has its level set $\left\{x: u(x) = u(0)\right\}$ diffeomorphic to an interval, then we prove the sharp bound $\kappa \leq 8$ on the curvature of the level set $\left\{x: u(x) = u(0)\right\}$ in the origin. The bound is sharp and we give the unique (up to symmetries) extremizer.
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math.SP 1years
2026 1verdicts
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Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries
Proves a generalised eigenvector expansion for infinite Toeplitz matrices with completely monotone entries, giving real eigenvalues and eigenvectors even when the matrix is not normal.