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On the difference equations with periodic coefficients. / Buslaev, V.; Fedotov, A.

в: Advances in Theoretical and Mathematical Physics, Том 5, № 6, 01.11.2001, стр. 1-45.

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Harvard

Buslaev, V & Fedotov, A 2001, 'On the difference equations with periodic coefficients', Advances in Theoretical and Mathematical Physics, Том. 5, № 6, стр. 1-45.

APA

Buslaev, V., & Fedotov, A. (2001). On the difference equations with periodic coefficients. Advances in Theoretical and Mathematical Physics, 5(6), 1-45.

Vancouver

Buslaev V, Fedotov A. On the difference equations with periodic coefficients. Advances in Theoretical and Mathematical Physics. 2001 Нояб. 1;5(6):1-45.

Author

Buslaev, V. ; Fedotov, A. / On the difference equations with periodic coefficients. в: Advances in Theoretical and Mathematical Physics. 2001 ; Том 5, № 6. стр. 1-45.

BibTeX

@article{fd622c30d12248728a0262916e989369,
title = "On the difference equations with periodic coefficients",
abstract = "In the paper, we study entire solutions of the difference equation ψ (z + h) = M (z) ψ (z), z ∈ C{double-struck}, ψ (z) ε C{double-struck}2. In this equation, h is a, fixed positive parameter, and M : C{double-struck} →SL (2, C{double-struck}) is a given matrix function. We assume that M(z) is a 2π-periodic trigonometric polynomial. The main aim is to construct the minimal entire solutions, e.i. the solutions with the minimal possible growth simultaneously as for z → -i∞ so for z → +i∞. We show that the monodromy matrices corresponding to the bases made of the minimal solutions are trigonometric polynomials of the same order as the matrix M. This property relates the spectral analysis of the one dimensional difference Schr{\"o}dinger equations with the potentials being trigonometric polynomials to an analysis of a finite dimensinal dynamical system.",
keywords = "Difference equations, Minimal entire solutions, Monodromy matrices, Renormalization",
author = "V. Buslaev and A. Fedotov",
year = "2001",
month = nov,
day = "1",
language = "English",
volume = "5",
pages = "1--45",
journal = "Advances in Theoretical and Mathematical Physics",
issn = "1095-0761",
publisher = "International Press of Boston, Inc.",
number = "6",

}

RIS

TY - JOUR

T1 - On the difference equations with periodic coefficients

AU - Buslaev, V.

AU - Fedotov, A.

PY - 2001/11/1

Y1 - 2001/11/1

N2 - In the paper, we study entire solutions of the difference equation ψ (z + h) = M (z) ψ (z), z ∈ C{double-struck}, ψ (z) ε C{double-struck}2. In this equation, h is a, fixed positive parameter, and M : C{double-struck} →SL (2, C{double-struck}) is a given matrix function. We assume that M(z) is a 2π-periodic trigonometric polynomial. The main aim is to construct the minimal entire solutions, e.i. the solutions with the minimal possible growth simultaneously as for z → -i∞ so for z → +i∞. We show that the monodromy matrices corresponding to the bases made of the minimal solutions are trigonometric polynomials of the same order as the matrix M. This property relates the spectral analysis of the one dimensional difference Schrödinger equations with the potentials being trigonometric polynomials to an analysis of a finite dimensinal dynamical system.

AB - In the paper, we study entire solutions of the difference equation ψ (z + h) = M (z) ψ (z), z ∈ C{double-struck}, ψ (z) ε C{double-struck}2. In this equation, h is a, fixed positive parameter, and M : C{double-struck} →SL (2, C{double-struck}) is a given matrix function. We assume that M(z) is a 2π-periodic trigonometric polynomial. The main aim is to construct the minimal entire solutions, e.i. the solutions with the minimal possible growth simultaneously as for z → -i∞ so for z → +i∞. We show that the monodromy matrices corresponding to the bases made of the minimal solutions are trigonometric polynomials of the same order as the matrix M. This property relates the spectral analysis of the one dimensional difference Schrödinger equations with the potentials being trigonometric polynomials to an analysis of a finite dimensinal dynamical system.

KW - Difference equations

KW - Minimal entire solutions

KW - Monodromy matrices

KW - Renormalization

UR - http://www.scopus.com/inward/record.url?scp=1542666173&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1542666173

VL - 5

SP - 1

EP - 45

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 6

ER -

ID: 35928289