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100 years of Weyl's law V. Ya. Ivrii Department of Mathematics, University of Toronto |
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Abstract: In 1911–1912 Hermann Weyl published two papers (more followed) describing the distribution of the eigenvalues of the Dirichlet Laplacian in a bounded domain. These were among the first publications by Weyl and a new exciting field of mathematics was created. I will discuss: • Weyl law with sharper remainder estimates (in particular, Weyl conjecture) • Generalized Weyl law • When the generalized Weyl law works and when it does not and how it should be modified • What should be used instead of the eigenvalue counting function when the spectrum is not necessarily discrete? • Weyl law and Thomas-Fermi theory • Some open problems. |
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