Journal of Soviet Mathematics

, Volume 28, Issue 1, pp 20–50 | Cite as

Matrix finite-zone operators

  • B. A. Dubrovin


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.


Spectral Property Explicit Formula Theta Function Algebraic Curf 
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© Plenum Publishing Corporation 1985

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  • B. A. Dubrovin

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