A Pincherle‐Type Convergence Theorem for Generalized Continued Fractions in Banach Algebras.
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| Title: | A Pincherle‐Type Convergence Theorem for Generalized Continued Fractions in Banach Algebras. |
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| Authors: | Baumann, Hendrik1 (AUTHOR) hendrik.baumann@uni-hildesheim.de, Hanschke, Thomas2 (AUTHOR), Hazra, Arpan (AUTHOR) ahazra@wiley.com |
| Source: | Journal of Applied Mathematics. 1/14/2026, Vol. 2026, p1-21. 21p. |
| Subjects: | Continued fractions, Banach algebras, Mathematics, Difference equations, Adjoint differential equations |
| Abstract: | This contribution is dedicated to the interdependence of higher order linear difference equations and generalized continued fractions in Banach algebras. It turns out that the computation of certain subdominant solutions of a higher order linear difference equation can be done more efficiently by considering its adjoint equation. The final result is a Pincherle‐type convergence criterion for generalized continued fractions in terms of the adjoint equation. To demonstrate the applicability of the method, it is applied to the Poincaré–Perron difference equation and selected problems from pure mathematics and applied stochastic processes. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 190910949 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Pincherle‐Type Convergence Theorem for Generalized Continued Fractions in Banach Algebras. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Baumann%2C+Hendrik%22">Baumann, Hendrik</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hendrik.baumann@uni-hildesheim.de</i><br /><searchLink fieldCode="AR" term="%22Hanschke%2C+Thomas%22">Hanschke, Thomas</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hazra%2C+Arpan%22">Hazra, Arpan</searchLink> (AUTHOR)<i> ahazra@wiley.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 1/14/2026, Vol. 2026, p1-21. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Continued+fractions%22">Continued fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Banach+algebras%22">Banach algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Difference+equations%22">Difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Adjoint+differential+equations%22">Adjoint differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This contribution is dedicated to the interdependence of higher order linear difference equations and generalized continued fractions in Banach algebras. It turns out that the computation of certain subdominant solutions of a higher order linear difference equation can be done more efficiently by considering its adjoint equation. The final result is a Pincherle‐type convergence criterion for generalized continued fractions in terms of the adjoint equation. To demonstrate the applicability of the method, it is applied to the Poincaré–Perron difference equation and selected problems from pure mathematics and applied stochastic processes. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/jama/5613612 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 1 Subjects: – SubjectFull: Continued fractions Type: general – SubjectFull: Banach algebras Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Difference equations Type: general – SubjectFull: Adjoint differential equations Type: general Titles: – TitleFull: A Pincherle‐Type Convergence Theorem for Generalized Continued Fractions in Banach Algebras. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Baumann, Hendrik – PersonEntity: Name: NameFull: Hanschke, Thomas – PersonEntity: Name: NameFull: Hazra, Arpan IsPartOfRelationships: – BibEntity: Dates: – D: 14 M: 01 Text: 1/14/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1110757X Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Journal of Applied Mathematics Type: main |
| ResultId | 1 |
