The strip of analyticity of reflectionless potentials

Ya. V. Mykytyuk; N. S. Sushchyk

doi:10.30970/ms.57.2.186-191

Ya. V. Mykytyuk Ivan Franko National University of Lviv, Lviv
N. S. Sushchyk Ivan Franko National University of Lviv, Lviv, Ukraine

DOI: https://doi.org/10.30970/ms.57.2.186-191

Keywords: bounded reflectionless potentials; Schrödinger operator; Bargmann potential.

Abstract

We study the problem of the analytical extension of bounded reflectionless potentials for
the Schrödinger operator in the Hilbert space $L_2(\mathbb{R})$ and improve an estimate on the strip of
analyticity established by V. A. Marchenko.

Author Biography

Ya. V. Mykytyuk, Ivan Franko National University of Lviv, Lviv

Department of Mechanics and Mathematics

References

V. Bargmann, On the connection between phase shifts and scattering potential, Rev. Mod. Phys., 21 (1949), 30–45.

V.A. Marchenko, The Cauchy problem for the KdV equation with nondecreasing initial data, in Whatintegrability?, Springer Ser. Nonlinear Dynam., Berlin: Springer, 1991, 273–318.

F. Calogero, A. Degasperis, Spectral transform and solitons: tools to solve and investigate nonlinear evolution equations, Amsterdam, New York: North-Holland, 1982.

R. Hryniv, B. Melnyk, Ya. Mykytyuk, Inverse scattering for reflectionless Schrödinger operators with integrable potentials and generalized soliton solutions for the KdV equation, Ann. Henri Poincare, 22 (2021), 487–527. https://doi.org/10.1007/s00023-020-01000-5