Аннотация:
Работа посвящена вопросу о геометрическом строении спектра оператора
Хилла с комплекснозначным потенциалом. Дана явная конструкция такого класса потенциалов, которым отвечают спектры, содержащие любое конечное число дуг, пересекающихся между собой во внутренних точках.
Библиогр. 11 назв.
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Fritz Gesztesy, Vadim Trachenko, “A criterion for Hill operators to be spectral operators of scalar type”, J Anal Math, 107:1 (2009), 287
Fritz Gesztesy, Vadim Tkachenko, “When is a non-self-adjoint Hill operator a spectral operator of scalar type?⁎⁎Based upon work supported by the US National Science Foundation under Grant No. DMS-0405526 and the Research Council and the Office of Research of the University of Missouri–Columbia.”, Comptes Rendus. Mathématique, 343:4 (2006), 239
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Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271
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Fritz Gesztesy, Rudi Weikard, “Picard potentials and Hill's equation on a torus”, Acta Math., 176:1 (1996), 73