Shabat, A. B. 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. Cited in 1 Document 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 Keywords:Schrödinger operator; Green’s function; additional spectrum; difference model PDF BibTeX XML Full Text: DOI References:  Shabat, A. B., No article title, Theor. Math. Phys., 183, 540-552, (2015) · Zbl 1317.37086  B. Levin, Lectures on Entire Functions, Amer. Math. Soc., New York (1996). · Zbl 0856.30001  Povzner, A., No article title, Mat. Sb., 23, 3-52, (1948)  Shabat, A. B., No article title, Funct. Anal. Appl., 9, 244-247, (1975) · Zbl 0352.34020  Barkina, U. V.; Melikhov, S. N., No article title, Vladikavkaz. Mat. Zh., 16, 27-40, (2014)  Shabat, A. B., No article title, Theor. Math. Phys., 179, 637-648, (2014) · Zbl 1329.34041  Dubrovin, B. A.; Matveev, V. B.; Novikov, S. P., No article title, Russ. Math. Surveys, 31, 59-146, (1976) · Zbl 0346.35025  Korotyaev, E., No article title, Inverse Problems, 21, 325-341, (2005) · Zbl 1074.34081 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.