Asymptotic approximations for second-order linear difference equations in Banach algebras, I
An asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras, subject to “finite moments perturbations.” The special case of linear matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and exp...
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| Published in | Journal of mathematical analysis and applications Vol. 337; no. 2; pp. 1158 - 1170 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
San Diego, CA
Elsevier Inc
15.01.2008
Elsevier |
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| Abstract | An asymptotic approximation theory is developed for some classes of linear second-order
difference equations in Banach algebras, subject to “finite moments perturbations.” The special case of linear
matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and explicitly computable bounds for the error terms are obtained. |
|---|---|
| AbstractList | An asymptotic approximation theory is developed for some classes of linear second-order
difference equations in Banach algebras, subject to “finite moments perturbations.” The special case of linear
matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and explicitly computable bounds for the error terms are obtained. |
| Author | Soldà, Tania Vianello, Marco Spigler, Renato |
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| Keywords | Finite moments asymptotics Matrix difference equations Banach algebras Second order equation Second order Error estimation Perturbation Difference equation Banach algebra Linear equation Mathematical analysis Approximation order Approximation theory Asymptotic approximation Application Matrix equation |
| Language | English |
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| References | T. Soldà, Approssimazione asintotica per equazioni alle differenze lineari del II ordine nelle algebre di Banach, Tesi di Laurea, Università di Padova, Padua, Italy, Academic Year 1996–1997 (in Italian) Agarwal (bib001) 2000; vol. 228 Spigler, Vianello (bib006) 1992; 169 Lakshmikantham, Trigiante (bib004) 1988 Hille (bib002) 1969 Spigler, Vianello (bib007) 1993; 119 Hille, Phillips (bib003) 1957; vol. 31 Hille (10.1016/j.jmaa.2007.04.054_bib003) 1957; vol. 31 10.1016/j.jmaa.2007.04.054_bib005 Spigler (10.1016/j.jmaa.2007.04.054_bib007) 1993; 119 Spigler (10.1016/j.jmaa.2007.04.054_bib006) 1992; 169 Agarwal (10.1016/j.jmaa.2007.04.054_bib001) 2000; vol. 228 Hille (10.1016/j.jmaa.2007.04.054_bib002) 1969 Lakshmikantham (10.1016/j.jmaa.2007.04.054_bib004) 1988 |
| References_xml | – volume: 169 start-page: 437 year: 1992 end-page: 452 ident: bib006 article-title: WKBJ-type approximation for finite moments perturbations of the differential equation publication-title: J. Math. Anal. Appl. – year: 1988 ident: bib004 article-title: Theory of Difference Equations: Numerical Methods and Applications – volume: vol. 31 year: 1957 ident: bib003 article-title: Functional Analysis and Semi-Groups publication-title: Amer. Math. Soc. Colloq. Publ. – volume: 119 start-page: 97 year: 1993 end-page: 103 ident: bib007 article-title: Finite moments perturbations of publication-title: Proc. Amer. Math. Soc. – year: 1969 ident: bib002 article-title: Lectures on Ordinary Differential Equations – reference: T. Soldà, Approssimazione asintotica per equazioni alle differenze lineari del II ordine nelle algebre di Banach, Tesi di Laurea, Università di Padova, Padua, Italy, Academic Year 1996–1997 (in Italian) – volume: vol. 228 year: 2000 ident: bib001 article-title: Difference Equations and Inequalities. Theory, Methods, and Applications publication-title: Monogr. Textbooks Pure Appl. Math. – volume: 169 start-page: 437 year: 1992 ident: 10.1016/j.jmaa.2007.04.054_bib006 article-title: WKBJ-type approximation for finite moments perturbations of the differential equation y″=0 and the analogous difference equation publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(92)90089-V – year: 1988 ident: 10.1016/j.jmaa.2007.04.054_bib004 – ident: 10.1016/j.jmaa.2007.04.054_bib005 – volume: vol. 228 year: 2000 ident: 10.1016/j.jmaa.2007.04.054_bib001 article-title: Difference Equations and Inequalities. Theory, Methods, and Applications – volume: vol. 31 year: 1957 ident: 10.1016/j.jmaa.2007.04.054_bib003 article-title: Functional Analysis and Semi-Groups – volume: 119 start-page: 97 year: 1993 ident: 10.1016/j.jmaa.2007.04.054_bib007 article-title: Finite moments perturbations of y″=0 in Banach algebras publication-title: Proc. Amer. Math. Soc. – year: 1969 ident: 10.1016/j.jmaa.2007.04.054_bib002 |
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| SubjectTerms | Algebra Banach algebras Difference and functional equations, recurrence relations Exact sciences and technology Finite differences and functional equations Finite moments asymptotics Functional analysis Linear and multilinear algebra, matrix theory Mathematical analysis Mathematics Matrix difference equations Numerical analysis Numerical analysis. Scientific computation Sciences and techniques of general use |
| Title | Asymptotic approximations for second-order linear difference equations in Banach algebras, I |
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