A study of some discrete Dirac equations with principal functions

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• 作者：T. Koprubasi ; R. N. Mohapatra
• 关键词：Key words and phrasesdiscrete Dirac equation ; spectral analysis ; eigenvalue ; principal function
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：150
• 期：2
• 页码：324-338
• 全文大小：692 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
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  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632
• 卷排序：150

文摘

Let L denote the operator generated in \({\ell _{2}( \mathbb{N}, \mathbb{C}^{2}) }\) by$$\left\{ \begin{array}{l}a_{n+1}y_{n+1}^{( 2) }+b_{n}y_{n}^{(2)}+p_{n}y_{n}^{( 1) }=\lambda y_{n}^{(1)} \\ a_{n-1}y_{n-1}^{(1)} +b_{n}y_{n}^{( 1) }+q_{n}y_{n}^{(2)} =\lambda y_{n}^{(2)},\end{array}\right.\quad n\in \mathbb{N} $$and the boundary condition$$(\gamma _{0}+\gamma _{1}\lambda +\gamma _{2}\lambda ^{2})y_{1}^{(2)}+(\beta_{0}+\beta _{1}\lambda +\beta _{2}\lambda ^{2})y_{0}^{(1)}=0$$where \({( a_{n})}\), \({( b_{n})}\), \({( p_{n}) }\) and \({( q_{n}) }\), \({n\in \mathbb{N} }\) are complex sequences, \({\gamma _{i},\beta _{i} \in \mathbb{C} }\), \({i=0,1,2}\) and \({\lambda }\) is a eigenparameter. With respect to the spectral properties of L, we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities of L, if$$\sum_{n=1}^{\infty }\exp (\varepsilon n^{\delta }) \big( |1-a_{n}| + |1+b_{n}| + |p_{n}| + |q_{n} | \big) < \infty $$holds for some \({\varepsilon > 0}\) and \({\delta \in [ \frac{1}{2},1] }\).Key words and phrasesdiscrete Dirac equationspectral analysiseigenvalueprincipal functionMathematics Subject Classification34L0534L4047A1047A75References1.Adivar M.: Quadratic pencil of difference equations: Jost solutions, spectrum, and principal vectors. Quaestiones Math. 33, 305–323 (2010)MathSciNetCrossRefMATHGoogle Scholar2.Adivar M., Bairamov E.: Spectral properties of non-selfadjoint difference operators. J. Math. Anal. Appl. 261, 461–478 (2001)MathSciNetCrossRefMATHGoogle Scholar3.Adivar M., Bohner M.: Spectral analysis of q-difference equations with spectral singularities. Math. Comput. Modelling 43, 695–703 (2006)MathSciNetCrossRefMATHGoogle Scholar4.Adivar M., Bohner M.: Spectrum and principal vectors of second order q-difference equations. Indian J. Math. 48, 17–33 (2006)MathSciNetMATHGoogle Scholar5.Bairamov E., Celebi A. O.: Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators. Quart. J. Math. Oxford Ser. (2) 50, 371–384 (1999)MathSciNetCrossRefMATHGoogle Scholar6.Bairamov E., Coskun C.: Jost solutions and the spectrum of the system of difference equations. Appl. Math. Lett. 17, 1039–1045 (2004)MathSciNetCrossRefMATHGoogle Scholar7.T. Koprubasi, Spectrum of the quadratic eigenparameter dependent discrete Dirac equations, Adv. Difference Equ., 148 (2014).8.Koprubasi T., Yokus N.: Quadratic eigenparameter dependent discrete Sturm Liouville equations with spectral singularities. Appl. Math. Comp. 244, 57–62 (2014)MathSciNetCrossRefMATHGoogle Scholar9.V. E. Lyance, A differential operator with spectral singularities, I, II, Amer. Math. Soc. Transl., 60 (1967), 185–225, 227–283.10.Naimark M. A.: Investigation of the spectrum and the expansion in eigenfunction of a non-selfadjoint operators of second order on a semi axis. Amer. Math. Soc. Transl. 16, 103–193 (1960)MathSciNetCrossRefGoogle ScholarCopyright information© Akadémiai Kiadó, Budapest, Hungary 2016Authors and AffiliationsT. Koprubasi12Email authorR. N. Mohapatra21.Department of MathematicsKastamonu UniversityKastamonuTurkey2.Department of MathematicsUniversity of Central FloridaOrlandoUSA About this article CrossMark Print ISSN 0236-5294 Online ISSN 1588-2632 Publisher Name Springer Netherlands About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s10474-016-0638-6_A study of some discrete Dirac equ", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s10474-016-0638-6_A study of some discrete Dirac equ", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. More information Accept Over 10 million scientific documents at your fingertips