Spectral theory of dissipative q-Sturm-Liouville problems

Aytekin Eryilmaz; Hüseyin Tuna

doi:10.1556/sscmath.51.2014.3.1289

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 51: Issue 3

Spectral theory of dissipative q-Sturm-Liouville problems

Authors:

Aytekin Eryilmaz

Aytekin Eryilmaz Nevşehir Haci Bektaş Veli University Department of Mathematics 50300 Nevşehir Turkey

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and

Hüseyin Tuna

Hüseyin Tuna Mehmet Akif Ersoy University Department of Mathematics 15100 Burdur Turkey

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Pages:: 366–383

Online Publication Date:: 26 Aug 2014

Publication Date:: 01 Sep 2014

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.51.2014.3.1289

Keywords:: Primary 47A20, 47A40, 47A45, 34L10, 33D15, 39A13; Sturm-Liouville operator; dilation; dissipative operator; completeness of the system of eigenvectors and associated vectors; scattering matrix; functional model; characteristic function

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This paper is devoted to studying a q-analogue of Sturm-Liouville operators. We formulate a dissipative q-difference operator in a Hilbert space. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which is based on the method of Pavlov and define its characteristic function. Finally, we prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative q-Sturm-Liouville difference operator.

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Studia Scientiarum Mathematicarum Hungarica

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András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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