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Periodic GMP Matrices
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Periodic GMP Matrices
Інший ID:
2010 Mathematics Subject Classification: 30E05; 30F15; 47B36; 42C05; 58J53
DOI:10.3842/SIGMA.2016.066
DOI:10.3842/SIGMA.2016.066
Посилання:
Periodic GMP Matrices / B. Eichinger // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
The author was supported by the Austrian Science Fund FWF, project no: P25591-N25. He
would like to thank his advisor Peter Yuditskii for his guidance and help during the preparation
of this paper. Finally, he is grateful to the anonymous referees for their remarks that improved
the presentation of the paper.
Дата:
2016
Переглядів:
439
Завантажень:
148
Анотація:
We recall criteria on the spectrum of Jacobi matrices such that the corresponding isospectral torus consists of periodic operators. Motivated by those known results for Jacobi matrices, we define a new class of operators called GMP matrices. They form a certain Generalization of matrices related to the strong Moment Problem. This class allows us to give a parametrization of almost periodic finite gap Jacobi matrices by periodic GMP matrices. Moreover, due to their structural similarity we can carry over numerous results from the direct and inverse spectral theory of periodic Jacobi matrices to the class of periodic GMP matrices. In particular, we prove an analogue of the remarkable ''magic formula'' for this new class.
