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Difference Schrödinger equation and quasisymmetric polynomials. (English. Russian original) Zbl 1329.81176
Theor. Math. Phys. 184, No. 2, 1067-1077 (2015); translation from Teor. Mat. Fiz. 184, No. 2, 200–211 (2015).
Summary: We study the singularity of solutions of the Schrödinger equation with a finite potential at the point $$k = 0$$. In the case of delta-type potentials, we show that the nature of this singularity is automodel in a certain sense. We discuss using the obtained results to construct an approximate solution of the inverse scattering problem on the whole axis. For this, we introduce the concept of a quasisymmetric polynomial associated with a given curve.

##### MSC:
 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 39A12 Discrete version of topics in analysis 35J08 Green’s functions for elliptic equations
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##### References:
 [1] Shabat, A. B., No article title, Theor. Math. Phys., 183, 540-552, (2015) · Zbl 1317.37086 [2] B. Levin, Lectures on Entire Functions, Amer. Math. Soc., New York (1996). · Zbl 0856.30001 [3] Povzner, A., No article title, Mat. Sb., 23, 3-52, (1948) [4] Shabat, A. B., No article title, Funct. Anal. Appl., 9, 244-247, (1975) · Zbl 0352.34020 [5] Barkina, U. V.; Melikhov, S. N., No article title, Vladikavkaz. Mat. Zh., 16, 27-40, (2014) [6] Shabat, A. B., No article title, Theor. Math. Phys., 179, 637-648, (2014) · Zbl 1329.34041 [7] Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P., No article title, Russ. Math. Surveys, 31, 59-146, (1976) · Zbl 0346.35025 [8] Korotyaev, E., No article title, Inverse Problems, 21, 325-341, (2005) · Zbl 1074.34081
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