В работе доказывается единственность и приведены достаточные условия разрешимости обратной задачи восстановления оператора диффузии по одному спектру.Ключевые слова: обратная задача, оператор диффузии, спектр.
It is well known that if ϕ(t) ≡ t, then the system {ϕ n (t)} ∞ n=0 is not a Schauder basis in L2[0, 1]. It is natural to ask whether there is a function ϕ for which the power system {ϕ n (t)} ∞ n=0 is a basis in some Lebesgue space Lp. The aim of this short note is to show that the answer to this question is negative.
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