{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:15:12Z","timestamp":1649063712538},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T00:00:00Z","timestamp":1397174400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/2.0"},{"start":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T00:00:00Z","timestamp":1397174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Differ Equ"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper, we first consider some new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek polynomials. In the second part, we investigate the oscillatory and boundedness properties of the related orthogonality measures and the functions representing them. The polynomials considered so far in this article are closely related to the concept of the Wess-Ruffing discretization.<\/jats:p>","DOI":"10.1186\/1687-1847-2014-110","type":"journal-article","created":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T17:10:06Z","timestamp":1397236206000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Oscillatory difference equations and moment problems"],"prefix":"10.1186","volume":"2014","author":[{"given":"Jos\u00e9 M","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"Ruffing","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,4,11]]},"reference":[{"key":"803_CR1","volume-title":"Orthogonal Polynomials","author":"G Szeg\u00f6","year":"1975","unstructured":"Szeg\u00f6 G Colloquium Publications 23. In Orthogonal Polynomials. Am. Math. Soc., Providence; 1975."},{"key":"803_CR2","unstructured":"Ruffing, A: Contributions to discrete Schr\u00f6dinger theory. Habilitationsschrift, Technische Universit\u00e4t M\u00fcnchen (2006)"},{"key":"803_CR3","volume-title":"Adv. Differ. Equ","author":"A Ruffing","year":"2009","unstructured":"Ruffing A, Meiler M, Bruder A: Some basic difference equations of Schr\u00f6dinger boundary value problems. Adv. Differ. Equ. 2009., 2009: Article ID 569803"},{"issue":"5","key":"803_CR4","doi-asserted-by":"publisher","first-page":"2354","DOI":"10.1063\/1.532869","volume":"40","author":"KA Penson","year":"1999","unstructured":"Penson KA, Solomon AI: New generalized coherent states. J. Math. Phys. 1999, 40(5):2354\u20132363. 10.1063\/1.532869","journal-title":"J. Math. Phys"},{"key":"803_CR5","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0375-9601(03)00732-1","volume":"313","author":"C Quesne","year":"2003","unstructured":"Quesne C, Penson KA, Tkachuk VM: Maths-type q -deformed coherent states for \"Equation missing\"  No EquationSource Format=\"TEX\", only image and EquationSource Format=\"MATHML\" . Phys. Lett. A 2003, 313: 29\u201336. 10.1016\/S0375-9601(03)00732-1","journal-title":"Phys. Lett. A"},{"key":"803_CR6","unstructured":"Quesne, C, Penson, KA, Tkachuk, VM: Geometrical and physical properties of maths-type q-deformed coherent states for \"Equation missing\"  No EquationSource Format=\"TEX\", only image and EquationSource Format=\"MATHML\"  and \"Equation missing\"  No EquationSource Format=\"TEX\", only image and EquationSource Format=\"MATHML\" . Preprint (2003)"},{"key":"803_CR7","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/S0375-9601(01)00554-0","volume":"288","author":"C Quesne","year":"2001","unstructured":"Quesne C: Completeness of photon-added squeezed vacuum and one-photon-states and of photon-added coherent states on a circle. Phys. Lett. A 2001, 288: 241\u2013250. 10.1016\/S0375-9601(01)00554-0","journal-title":"Phys. Lett. A"},{"key":"803_CR8","doi-asserted-by":"publisher","first-page":"9213","DOI":"10.1088\/0305-4470\/35\/43\/316","volume":"35","author":"C Quesne","year":"2002","unstructured":"Quesne C: New q -deformed coherent states with an explicitly known resolution of unity. J. Phys. A 2002, 35: 9213\u20139226. 10.1088\/0305-4470\/35\/43\/316","journal-title":"J. Phys. A"},{"key":"803_CR9","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/S0377-0427(02)00613-1","volume":"153","author":"A Ruffing","year":"2003","unstructured":"Ruffing A, Lorenz J, Ziegler K: Difference ladder operators for a harmonic Schr\u00f6dinger oscillator using unitary linear lattices. J. Comput. Appl. Math. 2003, 153: 395\u2013410. 10.1016\/S0377-0427(02)00613-1","journal-title":"J. Comput. Appl. Math"},{"key":"803_CR10","doi-asserted-by":"crossref","unstructured":"Robnik, M, Liu, J: Supersymmetric quantum Mechanics based on higher excited states II: a few new examples of isospectral partner potentials. Preprint CAMTP (1997)","DOI":"10.1088\/0305-4470\/30\/4\/028"},{"key":"803_CR11","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1088\/0305-4470\/30\/4\/028","volume":"30","author":"M Robnik","year":"1997","unstructured":"Robnik M: Supersymmetric quantum mechanics based on higher excited states. J. Phys. A 1997, 30: 1287\u20131294. 10.1088\/0305-4470\/30\/4\/028","journal-title":"J. Phys. A"},{"key":"803_CR12","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1143\/PTPS.139.404","volume":"139","author":"A Ruffing","year":"2000","unstructured":"Ruffing A: Exponential lattices as regularizers in quantum mechanics. Prog. Theor. Phys. Suppl. 2000, 139: 404\u2013413.","journal-title":"Prog. Theor. Phys. Suppl"},{"issue":"3","key":"803_CR13","first-page":"304","volume":"3","author":"A Ruffing","year":"2000","unstructured":"Ruffing A: Unexpected supermodels. Nonlinear Phenom. Complex Syst. 2000, 3(3):304\u2013312.","journal-title":"Nonlinear Phenom. Complex Syst"},{"issue":"1","key":"803_CR14","first-page":"41","volume":"3","author":"A Ruffing","year":"2008","unstructured":"Ruffing A, Meiler M: Constructing similarity solutions to discrete basic diffusion equations. Adv. Dyn. Syst. Appl. 2008, 3(1):41\u201351.","journal-title":"Adv. Dyn. Syst. Appl"},{"issue":"2","key":"803_CR15","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1023\/A:1007378122623","volume":"42","author":"A Ruffing","year":"1997","unstructured":"Ruffing A, Witt M: On the integrability of q -oscillators based on invariants of discrete Fourier transforms. Lett. Math. Phys. 1997, 42(2):167\u2013181. 10.1023\/A:1007378122623","journal-title":"Lett. Math. Phys"},{"key":"803_CR16","series-title":"NATO Science Series II 30","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/978-94-010-0818-1_14","volume-title":"Special Functions 2000: Current Perspective and Future Directions","author":"VP Spiridonov","year":"2001","unstructured":"Spiridonov VP, Zhedanov AS: Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids. NATO Science Series II 30. In Special Functions 2000: Current Perspective and Future Directions. Edited by: Bustoz J, Ismail MEH, Suslov SK. Kluwer Academic, Dordrecht; 2001:365\u2013388."},{"key":"803_CR17","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1006\/aima.1998.1728","volume":"137","author":"B Simon","year":"1998","unstructured":"Simon B: The classical moment problem as a self-adjoint finite difference operator. Adv. Math. 1998, 137: 82\u2013203. 10.1006\/aima.1998.1728","journal-title":"Adv. Math"},{"issue":"11-12","key":"803_CR18","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1080\/10236190902877764","volume":"15","author":"JM Ferreira","year":"2009","unstructured":"Ferreira JM, Pinelas S, Ruffing A: Nonautonomous oscillators and coefficient evaluation for orthogonal function systems. J.\u00a0Differ. Equ. Appl. 2009, 15(11\u201312):1117\u20131133. 10.1080\/10236190902877764","journal-title":"J.\u00a0Differ. Equ. Appl"},{"key":"803_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325937","volume-title":"Special Functions","author":"GE Andrews","year":"1999","unstructured":"Andrews GE, Askey R, Roy R Encyclopedia of Mathematics and Its Applications. In Special Functions. Cambridge University Press, Cambridge; 1999."}],"container-title":["Advances in Difference Equations"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-1847-2014-110.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/1687-1847-2014-110\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-1847-2014-110.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T16:05:22Z","timestamp":1630598722000},"score":1,"resource":{"primary":{"URL":"https:\/\/advancesindifferenceequations.springeropen.com\/articles\/10.1186\/1687-1847-2014-110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,11]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["803"],"URL":"https:\/\/doi.org\/10.1186\/1687-1847-2014-110","relation":{},"ISSN":["1687-1847"],"issn-type":[{"value":"1687-1847","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,11]]},"assertion":[{"value":"2 June 2013","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 February 2014","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2014","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"110"}}