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

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Measurability of eigenelements $s \mapsto (\varphi_k(s), \lambda_k(s))$ of Laplace-Beltrami ...

For each $s \in [a,b]$, let $M_s$ be a compact Riemannian manifold with no boundary. Under what conditions on $s \mapsto M_s$ do the eigenvalues and eigenfunctions $(\varphi_k(s), \lambda_k(s))_{k \ …
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