Discrete symplectic systems, boundary triplets, and
self-adjoint extensions

J 2022

Discrete symplectic systems, boundary triplets, and self-adjoint extensions

ZEMÁNEK, Petr a Stephen L. CLARK

Základní údaje

Originální název

Discrete symplectic systems, boundary triplets, and self-adjoint extensions

Autoři

ZEMÁNEK, Petr a Stephen L. CLARK

Vydání

Dissertationes Mathematicae, Warszawa, Institute of Mathematics. Polish Academy of Sciences, 2022, 0012-3862

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Polsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.800

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00129119

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

discrete symplectic system; linear relation; self-adjoint extension; boundary triplets

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 12. 8. 2022 15:43, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

An explicit characterization of all self-adjoint extensions of the minimal linear relation associated with a discrete symplectic system is provided using the theory of boundary triplets with special attention paid to the quasiregular and limit point cases. A particular example of the system (the second order Sturm–Liouville difference equation) is also investigated thoroughly, while higher order equations or linear Hamiltonian difference systems are discussed briefly. Moreover, the corresponding gamma field and Weyl relations are established and their connection with the Weyl solution and the classical M(λ)-function is discussed. To make the paper reasonably self-contained, an extensive introduction to the theory of linear relations, self-adjoint extensions, and boundary triplets is included.

Návaznosti

GA19-01246S, projekt VaV

Název: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Grantová agentura ČR, Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Citovat

ZEMÁNEK, Petr a Stephen L. CLARK. Discrete symplectic systems, boundary triplets, and self-adjoint extensions. Dissertationes Mathematicae. Warszawa: Institute of Mathematics. Polish Academy of Sciences, 2022, roč. 579, May, s. 1-87. ISSN 0012-3862. Dostupné z: https://doi.org/10.4064/dm838-12-2021.

@article{1875997,
   author = {Zemánek, Petr and Clark, Stephen L.},
   article_location = {Warszawa},
   article_number = {May},
   doi = {https://doi.org/10.4064/dm838-12-2021},
   keywords = {discrete symplectic system; linear relation; self-adjoint extension; boundary triplets},
   language = {eng},
   issn = {0012-3862},
   journal = {Dissertationes Mathematicae},
   title = {Discrete symplectic systems, boundary triplets, and self-adjoint extensions},
   url = {https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/114677/discrete-symplectic-systems-boundary-triplets-and-self-adjoint-extensions},
   volume = {579},
   year = {2022}
}

TY  - JOUR
ID  - 1875997
AU  - Zemánek, Petr - Clark, Stephen L.
PY  - 2022
TI  - Discrete symplectic systems, boundary triplets, and self-adjoint extensions
JF  - Dissertationes Mathematicae
VL  - 579
IS  - May
SP  - 1-87
EP  - 1-87
PB  - Institute of Mathematics. Polish Academy of Sciences
SN  - 00123862
KW  - discrete symplectic system
KW  - linear relation
KW  - self-adjoint extension
KW  - boundary triplets
UR  - https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/114677/discrete-symplectic-systems-boundary-triplets-and-self-adjoint-extensions
N2  - An explicit characterization of all self-adjoint extensions of the minimal linear relation associated with a discrete symplectic system is provided using the theory of boundary triplets with special attention paid to the quasiregular and limit point cases. A particular example of the system (the second order Sturm–Liouville difference equation) is also investigated thoroughly, while higher order equations or linear Hamiltonian difference systems are discussed briefly. Moreover, the corresponding gamma field and Weyl relations are established and their connection with the Weyl solution and the classical M(λ)-function is discussed. To make the paper reasonably self-contained, an extensive introduction to the theory of linear relations, self-adjoint extensions, and boundary triplets is included.
ER  -

ZEMÁNEK, Petr a Stephen L. CLARK. Discrete symplectic systems, boundary triplets, and self-adjoint extensions. \textit{Dissertationes Mathematicae}. Warszawa: Institute of Mathematics. Polish Academy of Sciences, 2022, roč.~579, May, s.~1-87. ISSN~0012-3862. Dostupné z: https://doi.org/10.4064/dm838-12-2021.

Přehled o publikaci