Some inequalities for Laplace eigenfunctions and their gradients

Abstract: We will survey some recent results on restrictions of Laplace eigenfunctions and present new norm inequalities for the eigenfunctions and their gradients obtained in a joint work with Stefano Decio. The guiding principle, which goes back to the works of Donnelly and Fefferman, is that eigenfunctions with eigenvalue $\textrm{E}^2$ behave like (harmonic) polynomials of degree $\textrm{E}$.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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