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- W2088602743 abstract "Weyl–Titchmarsh matrix functions play an essential role in the spectral theory of Dirac-type equations (Oper. Theory: Adv. Appl.107 (1999)). In this paper, we have constructed a class of Weyl–Titchmarsh matrix-functions generating potentials of finite-zone type. It has turned out that the corresponding potentials have derivatives of an arbitrary order. Using the above-mentioned results, we deduce the matrix analogue of the trace formula for finite-zone matrix potentials. In the last part of the paper, we consider separately the scalar case of Dirac-type equations. For this case, we have constructed finite-zone potentials in explicit forms and proved that these potentials are quasiperiodical. We note that for scalar Schrödinger equations the corresponding results are well known (see Invent. Math.30 (1975), 217–274; “Soliton and the Inverse Scattering Transform,” SIAM, Philadelphia, 1981; Rev. Sci. Technol.23 (1983), 20–50; “Theory of Solitons, The Method of Inverse Problem,” New York, 1984; “Inverse Sturm–Liouville Problems,” VSP, Zeist, 1987; “Inverse Spectral Theory,” Academic Press, New York, 1987)." @default.
- W2088602743 created "2016-06-24" @default.
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- W2088602743 date "2002-08-01" @default.
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- W2088602743 title "Matrix Finite-Zone Dirac-Type Equations" @default.
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- W2088602743 doi "https://doi.org/10.1006/jfan.2002.3956" @default.
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