Block Jacobi matrices and Titchmarsh-Weyl function
We collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case. We focus here on some issues related to the matrix Titchmarsh-Weyl function, but we also co...
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AGH Univeristy of Science and Technology Press
2025-05-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4518.pdf |
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| author | Marcin Moszyński Grzegorz Świderski |
| author_facet | Marcin Moszyński Grzegorz Świderski |
| author_sort | Marcin Moszyński |
| collection | DOAJ |
| description | We collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case. We focus here on some issues related to the matrix Titchmarsh-Weyl function, but we also consider generalizations of some other tools used by subordinacy theory, including the matrix orthogonal polynomials, the notion of finite cyclicity, a variant of a notion of nonsubordinacy, as well as Jitomirskaya-Last type semi-norms. The article brings together some issues already known, our new concepts, and also improvements and strengthening of some results already existing. We give simpler proofs of some known facts, or we add details usually omitted in the existing literature. The introduction contains a separate part devoted to a brief review of the main spectral analysis methods used so far for block Jacobi operators. |
| format | Article |
| id | doaj-art-dab4ea99bcd44b6e9575a0b2d26f88d2 |
| institution | DOAJ |
| issn | 1232-9274 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj-art-dab4ea99bcd44b6e9575a0b2d26f88d22025-08-20T03:21:38ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742025-05-01453351402https://doi.org/10.7494/OpMath.2025.45.3.3514518Block Jacobi matrices and Titchmarsh-Weyl functionMarcin Moszyński0https://orcid.org/0000-0002-9268-1303Grzegorz Świderski1https://orcid.org/0000-0003-4372-2989University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, ul. Stefana Banacha 2, 02-097 Warsaw, PolandPolish Academy of Sciences, Institute of Mathematics, ul. Śniadeckich 8, 00-696 Warsaw, PolandWe collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case. We focus here on some issues related to the matrix Titchmarsh-Weyl function, but we also consider generalizations of some other tools used by subordinacy theory, including the matrix orthogonal polynomials, the notion of finite cyclicity, a variant of a notion of nonsubordinacy, as well as Jitomirskaya-Last type semi-norms. The article brings together some issues already known, our new concepts, and also improvements and strengthening of some results already existing. We give simpler proofs of some known facts, or we add details usually omitted in the existing literature. The introduction contains a separate part devoted to a brief review of the main spectral analysis methods used so far for block Jacobi operators.https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4518.pdfblock jacobi matrixmatrix measurestitchmarsh-weyl functionliouville-ostrogradsky formulae |
| spellingShingle | Marcin Moszyński Grzegorz Świderski Block Jacobi matrices and Titchmarsh-Weyl function Opuscula Mathematica block jacobi matrix matrix measures titchmarsh-weyl function liouville-ostrogradsky formulae |
| title | Block Jacobi matrices and Titchmarsh-Weyl function |
| title_full | Block Jacobi matrices and Titchmarsh-Weyl function |
| title_fullStr | Block Jacobi matrices and Titchmarsh-Weyl function |
| title_full_unstemmed | Block Jacobi matrices and Titchmarsh-Weyl function |
| title_short | Block Jacobi matrices and Titchmarsh-Weyl function |
| title_sort | block jacobi matrices and titchmarsh weyl function |
| topic | block jacobi matrix matrix measures titchmarsh-weyl function liouville-ostrogradsky formulae |
| url | https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4518.pdf |
| work_keys_str_mv | AT marcinmoszynski blockjacobimatricesandtitchmarshweylfunction AT grzegorzswiderski blockjacobimatricesandtitchmarshweylfunction |