Dirac systems with regular and singular transmission effects | Zendy

Ekin Uğurlu | Zendy

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Dirac systems with regular and singular transmission effects

Author(s) -

Ekin Uğurlu

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1601-70

Subject(s) - mathematics , dissipative system , dissipative operator , hilbert space , equivalence (formal languages) , transmission (telecommunications) , pure mathematics , mathematical analysis , spectral theory , quantum mechanics , physics , electrical engineering , engineering

In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl’s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax–Phillips scattering function and Sz-Nagy–Foiaş characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.

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