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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

3 votes
0 answers
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 …