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Prymians of real curves and their applications to the effectivization of Schrödinger operators. (English. Russian original) Zbl 0682.35027
Funct. Anal. Appl. 23, No. 1, 33-45 (1989); translation from Funkts. Anal. Prilozh. 23, No. 1, 41-56 (1989).
A. P. Veselov and S. P. Novikov [Sov. Math., Dokl. 30, 588- 591 (1984); translation from Dokl. Akad. Nauk SSSR 279, 20-24 (1984; Zbl 0613.35020); and ibid., 705-708 (1984); translation from Dokl. Akad. Nauk SSSR 279, 784-788 (1984; Zbl 0602.35024)] describe the class of real two- dimensional Schrödinger operators \[ L=\partial {\bar \partial}+2\partial {\bar \partial} \ell n \theta (zU_ 1+\bar zU_ 2- e| V)-\epsilon_ 0, \] where \(\theta\) denotes Prym’s theta-function of real algebraic curve with involutions. Present paper gives the effective description of Prym’s variety of real curves and special properties of holomorphical differentials on real curves.
Reviewer: S.M.Natanzon

MSC:
35J10 Schrödinger operator, Schrödinger equation
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