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

3 votes
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399 views

Smooth perturbation of a positive self-adjoint operator with compact resolvent

Consider a one-parameter family $A_t$ of unbounded positive self-adjoint operators with discrete spectrum (for example, one can consider a one-parameter family of Laplacians on a compact Riemannian ma …