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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > $L_1$-Estimates for Eigenfunctions of the Dirichlet Laplacian

## $L_1$-Estimates for Eigenfunctions of the Dirichlet LaplacianAdd to your list(s) Download to your calendar using vCal - Hempel, R (Technische Universitt Braunschweig)
- Wednesday 24 June 2015, 15:00-16:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact webseminars. Periodic and Ergodic Spectral Problems Co-authors: Michiel van den Berg (U Bristol), J”urgen Voigt (TU Dresden) For $d in {f N}$ and $Omega e mptyset$ an open set in ${f R}^d$, we consider the eigenfunctions $Phi$ of the Dirichlet Laplacian $-Delta_Omega$ of $Omega$. We do {it not} require $Omega$ to be of finite volume. % If $Phi$ is associated with an eigenvalue below the essential spectrum of $-Delta_Omega$, we provide estimates for the $L_1$-norm of $Phi$ in terms of the $L_2$-norm of $Phi$ and suitable spectral data of $-Delta_Omega$. The main idea in obtaining such estimates consists in finding a—-sufficiently small—-subset $Omega’ ubset Omega$ where $Phi$ is localized in the sense that $Phi$ decays exponentially as one moves away from $Omega’$.
skip.5em This is joint work with Michiel van den Berg (Bristol) and J”urgen Voigt (Dresden), with improvements by Hendrik Vogt (Dresden). This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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