Об аналитических свойствах функции Вейля оператора Штурма – Лиувилля с комплексным убывающим потенциалом

TL;DRAbstract

We study the spectral properties of the operator L_ associated with the quadratic form L_ = 1R 0 (|y0|2 − _x−|y|2)dx with the domain Q0 = {y 2 W1 2 (0,+1) : y(0) = 0}, 0 0, = 1 and for real W satisfying a more strict decaying condition at infinity. The main result of the paper is the proof of necessity (with some reservations) of the sufficient conditions for W(x) obtained earlier by Kh.Kh. Murtazin under which the Weyl function of the operator M_ possesses an analytic continuation on some angle from non-physical sheet.

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