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Register a new userMoutard type transformation for matrix generalized analytic functions and gauge transformations
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A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.
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P.G. Grinevich L.D. Landau Institute forn Theoretical Physics
, Lomonosov Moscow State University
2015
We continue the studies of Moutard-type transform for generalized analytic functions started in our previous paper: arXiv:1510.08764. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that in the framework of this approach Moutard-type transforms for the aforementioned functions commute with holomorphic changes of variables.
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P.G. Grinevich L.D. Landau Institute forn Theoretical Physics
, Lomonosov Moscow State University
2015
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.
271 -
P.G. Grinevich L.D. Landau Institute forn Theoretical Physics
, Lomonosov Moscow State University
2015
We continue studies of Moutard-type transforms for the generalized analytic functions started in arXiv:1510.08764, arXiv:1512.00343. In particular, we show that generalized analytic functions with the simplest contour poles can be Moutard transformed to the regular ones, at least, locally. In addition, the later Moutard-type transforms are locally invertible.
Formulas relating Poincare-Steklov operators for Schroedinger equations related by Darboux-Moutard transformations are derived. They can be used for testing algorithms of reconstruction of the potential from measurements at the boundary.
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning commutation with rotation, continuation beyond the domain of univalence, and periodicity.
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