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Uniform perturbation theory for selfadjoint operators
A spectral characterization problem
3 other sections not shown
an(u arbitrary assertion assume assumption Banach space bounded CC)i closed and symmetric consider continuous functions continuous map Corollary CS(X define denote eigenfunction eigenvalue of A(u eigenvalue problems eigenvectors equation Euler-Lagrange equation following properties functional Gn(X Grassmannian Hausdorff distance Hence Hilbert space homeomorphism ICs(X implies infer ip(u Lemma lower semicontinuous minimax minimizing sequence Moreover Nehari nn(u nodal nonlinear norm notation odd and continuous operator G(u paracompact particular pn(u precisely problem SC)n Proof Prop Proposition 2.8 Proposition 6.24 pu(u pu(v radial projection relatively compact remark resp scalar product Section selfadjoint simple zeroes solution of SC)n Solutions with prescribed spectral projection associated strongly continuous Sturm-Liouville problems sublinear subspace sup inf superlinear Suppose symmetric subset Theorem topological tp(u uj)j Un(X unit sphere weakly yields zeroes in 0,1