$L_1$-estimates for eigenfunctions of the Dirichlet Laplacian
نویسندگان
چکیده
منابع مشابه
L1-Estimates for Eigenfunctions of the Dirichlet Laplacian
For d ∈ N and Ω 6= ∅ an open set in R, we consider the eigenfunctions Φ of the Dirichlet Laplacian −∆Ω of Ω. If Φ is associated with an eigenvalue below the essential spectrum of −∆Ω we provide estimates for the L1-norm of Φ in terms of its L2-norm and spectral data. These L1estimates are then used in the comparison of the heat content of Ω at time t > 0 and the heat trace at times t′ > 0, wher...
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ژورنال
عنوان ژورنال: Journal of Spectral Theory
سال: 2015
ISSN: 1664-039X
DOI: 10.4171/jst/115