Convexity Property and Applications
نویسنده
چکیده
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property 13 of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators 15 that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the present paper are illustrated by several exam17 ples from mechanics or quantum mechanics, including the Sturm–Liouville problem, the Schrödinger equation, and the harmonic oscillator. 19
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