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- W2950255181 abstract "For $d in N$ and $Omega ne emptyset$ an open set in $R^d$, we consider the eigenfunctions $Phi$ of the Dirichlet Laplacian $-Delta_Omega$ of $Omega$. 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 its $L_2$-norm and spectral data. These $L_1$-estimates are then used in the comparison of the heat content of $Omega$ at time $t>0$ and the heat trace at times $t' > 0$, where a two-sided estimate is established. We furthermore show that all eigenfunctions of $-Delta_Omega$ which are associated with a discrete eigenvalue of $H_Omega$, belong to $L_1(Omega)$." @default.
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- W2950255181 date "2013-08-22" @default.
- W2950255181 modified "2023-09-27" @default.
- W2950255181 title "L_1-Estimates for Eigenfunctions of the Dirichlet Laplacian" @default.
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