By A. Kufner, Oldrich John, Svatopluk Fucik
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Lemma. Let E ∈ HB and d : R → N0 . (i) Let ω ∈ Admd (E). Then ω/ is minimal in Admd (E)/ if and only if ω/ is minimal in Adm(E)/ . (ii) The set Admd (E)/ contains at most one minimal element. Proof. 7]. 4]. We can now settle the question when, and in which way, finite-dimensional de Branges subspaces can be represented by majorants. Put R(E) := Rω (E) : ω ∈ Adm(E) . 8. Theorem. Let E ∈ HB and d : R → N0 . Then the following conditions are equivalent: (i) Admd (E)/ contains a minimal element; (ii) FSubd (E) ∩ R(E) = ∅; (iii) FSubd (E) = ∅ and Subd (E) ⊆ R(E).
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