Spectral Analysis of Certain Schrödinger Operators

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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dc.contributor.author	Ismail, Mourad E.H.
dc.contributor.author	Koelink, E
dc.date.accessioned	2019-02-18T13:10:40Z
dc.date.available	2019-02-18T13:10:40Z
dc.date.issued	2012
dc.identifier.citation	Spectral Analysis of Certain Schrödinger Operators / Mourad E.H. Ismail, E. Koelink // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 40 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 30E05; 33C45; 39A10; 42C05; 44A60
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.061
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148463
dc.description.abstract	The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages].	uk_UA
dc.description.sponsorship	The research of Mourad E.H. Ismail is supported by a Research Grants Council of Hong Kong under contract # 101411 and NPST Program of King Saud University, Saudi Arabia, 10-MAT 1293-02. This work was also partially supported by a grant from the ‘Collaboration Hong Kong –Joint Research Scheme’ sponsored by the Netherlands Organisation of Scientific Research and the Research Grants Council for Hong Kong (Reference number: 600.649.000.10N007). The work for this paper was done while both authors visited City University Hong Kong, and we are grateful for the hospitality. We thank Luc Vinet and Hocine Bahlouli for useful comments and references. We also thank the referees for their very careful reading and for their suggestions and constructive criticism that have improved the paper.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Spectral Analysis of Certain Schrödinger Operators	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA