### Abstract

Language | English |
---|---|

Number of pages | 9 |

Journal | Mathematische Nachrichten |

Early online date | 4 Jul 2018 |

DOIs | |

Publication status | E-pub ahead of print - 4 Jul 2018 |

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### Keywords

- boundary system
- boundary triple
- boundary triplet
- deficiency index
- extension problem

### Cite this

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**Some remarks on the notions of boundary systems and boundary triple(t)s.** / Waurick, Marcus; Wegner, Sven-Ake.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Some remarks on the notions of boundary systems and boundary triple(t)s

AU - Waurick, Marcus

AU - Wegner, Sven-Ake

PY - 2018/7/4

Y1 - 2018/7/4

N2 - In this note we show that if a boundary system in the sense of (Schubert et al. 2015) gives rise to any skew‐self‐adjoint extension, then it induces a boundary triplet and the classification of all extensions given by (Schubert et al. 2015) coincides with the skew‐symmetric version of the classical characterization due to (Gorbachuk et al. 1991). On the other hand we show that for every skew‐symmetric operator there is a natural boundary system which leads to an explicit description of at least one maximal dissipative extension. This is in particular also valid in the case that no boundary triplet exists for this operator.

AB - In this note we show that if a boundary system in the sense of (Schubert et al. 2015) gives rise to any skew‐self‐adjoint extension, then it induces a boundary triplet and the classification of all extensions given by (Schubert et al. 2015) coincides with the skew‐symmetric version of the classical characterization due to (Gorbachuk et al. 1991). On the other hand we show that for every skew‐symmetric operator there is a natural boundary system which leads to an explicit description of at least one maximal dissipative extension. This is in particular also valid in the case that no boundary triplet exists for this operator.

KW - boundary system

KW - boundary triple

KW - boundary triplet

KW - deficiency index

KW - extension problem

UR - https://arxiv.org/abs/1710.10823

UR - https://onlinelibrary.wiley.com/journal/15222616

U2 - 10.1002/mana.201700417

DO - 10.1002/mana.201700417

M3 - Article

JO - Mathematische Nachrichten

T2 - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

ER -