Dual variational approaches to multiparameter eigenvalue problems
Journal of Mathematical Analysis and Applications, 1983 AbstractWe study the abstract multiparameter problem Tmxm = ∑kn=1 λn Vmnxm, 0 ≠ xm ϵ Hm, m = 1,…, k, for selfadjoint operators Tm and Vmn on separable Hilbert spaces Hm. We develop dual variational approaches related to the polar duality between certain convex sets. The “primal” approach has been the basis of several investigations, particularly in the
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