A survey is given of the spectral properties of matrix finite-zone operators. Conditions of the type of J-self-adjointness for such operators and explicit formulas expressing the coefficients of such operators in terms of theta functions are obtained. The simplest examples of such J-self-adjoint, finite-zone operators turn out to be connected with the theory of ovals of plane, real, algebraic curves.
Matrix finite-gap operators / Dubrovin, Boris. - In: JOURNAL OF SOVIET MATHEMATICS. - ISSN 0090-4104. - 28:1(1985), pp. 20-50.
Matrix finite-gap operators
Dubrovin, Boris
1985-01-01
Abstract
A survey is given of the spectral properties of matrix finite-zone operators. Conditions of the type of J-self-adjointness for such operators and explicit formulas expressing the coefficients of such operators in terms of theta functions are obtained. The simplest examples of such J-self-adjoint, finite-zone operators turn out to be connected with the theory of ovals of plane, real, algebraic curves.File in questo prodotto:
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