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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

5 votes
3 answers
972 views

Boundedness of Laplacian eigenfunctions

Let $A$ be a bounded domain in $\mathbb R^d$, $d>1$, and $\{u_k\}$ is the set of all $L^2$-normalized Laplacian eigenfunctions on $A$ with Dirichlet boundary condition (i.e., $\|u_k\|_2 = 1$). Is it …
Denis Grebenkov's user avatar
3 votes
2 answers
638 views

Localization of Laplacian eigenfunction on the unit square?

Let A be the unit square, $\{u_k\}$ is the set of all L2-normalized Laplacian eigenfunctions with Dirichlet boundary condition. Is it true that for any open subset V, $C_V = \inf\limits_k \int\limits_ …
Denis Grebenkov's user avatar