M-dissipative boundary conditions and boundary tuples for Maxwell operators

Eller, Matthias; Karabash, Illya M.

doi:10.1016/j.jde.2022.04.006

Journal of Differential Equations

2022

DOI: 10.1016/j.jde.2022.04.006

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M-dissipative boundary conditions and boundary tuples for Maxwell operators

Matthias Eller

Illya M. Karabash

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2024

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Quasi Gelfand Triples

Skrepek

2024

Integr. Equ. Oper. Theory

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We generalize the notion of Gelfand triples (also called Banach-Gelfand triples or rigged Hilbert spaces) by dropping the necessity of a continuous embedding. This means in our setting we lack of a chain inclusion. We replace the continuous embedding by a closed embedding of a dense subspace. This notion will be called quasi Gelfand triple. These triples appear naturally, when we regard the boundary spaces of spatially multidimensional differential operators, e.g., the Maxwell operator. We will show that there is a smallest space where we can continuously embed the entire triple. Moreover, we will show density results for intersections of members of the quasi Gelfand triple. Finally, we show that every quasi Gelfand triple can be decomposed into two “ordinary” Gelfand triples.

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Quasi Gelfand Triples

Skrepek

2024

Integr. Equ. Oper. Theory

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M-dissipative boundary conditions and boundary tuples for Maxwell operators

Cited by 1 publication

References 73 publications

Quasi Gelfand Triples

Quasi Gelfand Triples

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