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Mat. Zametki, 2022 Volume 111, Issue 6, Pages 846–863 (Mi mzm13429)

On Scattering Data for Differential Systems with a Singularity

M. Yu. Ignat'ev

Saratov State University

Abstract: We study the characteristic properties of scattering data for the differential system with a singularity $y'-x^{-1}Ay-q(x)y=\rho By$ in the case of an integrable potential $q(\,\cdot\,)$. Structural and analytical properties are established for the conjugation matrix – a part of the scattering data related to the continuous spectrum.

Keywords: scattering problems, differential systems, singularity.

UDC: 517.984

Received: 20.01.2022

DOI: 10.4213/mzm13429


 English version:
Mathematical Notes, 2022, 111:6, 879–893

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© Steklov Math. Inst. of RAS, 2024