Sturm-Liouville boundary value problems and Lagrange interpolation series
This paper is concerned with the connection between the Kramer sampling theorem and one form of the Lagrange interpolation formula. One particular interest of this connection is when the Kramer-type kernel has certain analytic properties since this leads to corresponding analyticity for the individu...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1994-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(1)/87-126.pdf |
| _version_ | 1797814074990395392 |
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| author | W.N. EVERITT G. SCHOTTLER P.L. BUTZER |
| author_facet | W.N. EVERITT G. SCHOTTLER P.L. BUTZER |
| author_sort | W.N. EVERITT |
| collection | DOAJ |
| description | This paper is concerned with the connection between the Kramer sampling theorem and one form of the Lagrange interpolation formula. One particular interest of this connection is when the Kramer-type kernel has certain analytic properties since this leads to corresponding analyticity for the individual terms in the Lagrange
interpolation series. Recent results have shown that one important and significant case of this connection is to be found in the generation of these Kramer-type kernels from self-adjoint boundary value problems, determined by symmetric ordinary linear differential expressions defined on intervals of the real line. In these cases the analyticity properties result from the presence of the spectral parameter of the corresponding selfadjoint differential operator. Results in this paper are restricted to consideration of the classic Sturm-Liouville differential expression of the second-order, but under the minimal (locally Lebesgue integrable) conditions on the coefficients; furthermore the expression is taken to be in the regular and/or limit-circle end-point classification.
This approach follows earlier work of Weiss, Kramer, Campbell and others, and
recent results of Butzer, Zayed and Schottler. The new methods adopted here should
extend to other end-point classifications and to symmetric differential expressions of
arbitrary order.
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| first_indexed | 2024-03-13T08:01:09Z |
| format | Article |
| id | doaj.art-63726b9ae9004d6291d0245bce3cc84b |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-03-13T08:01:09Z |
| publishDate | 1994-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-63726b9ae9004d6291d0245bce3cc84b2023-06-01T14:25:05ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501994-01-0114187126Sturm-Liouville boundary value problems and Lagrange interpolation seriesW.N. EVERITT0 G. SCHOTTLER1 P.L. BUTZER2 School of Mathematics and Statistics - University of Birmingham - Birmingham B15 2TT - England - UKLehrstuhl A fur Mathematik - RWTH Aachen - Templergraben 55 - 52056 Aachen - GermanyLehrstuhl A fur Mathematik - RWTH Aachen - Templergraben 55 - 52056 Aachen - GermanyThis paper is concerned with the connection between the Kramer sampling theorem and one form of the Lagrange interpolation formula. One particular interest of this connection is when the Kramer-type kernel has certain analytic properties since this leads to corresponding analyticity for the individual terms in the Lagrange interpolation series. Recent results have shown that one important and significant case of this connection is to be found in the generation of these Kramer-type kernels from self-adjoint boundary value problems, determined by symmetric ordinary linear differential expressions defined on intervals of the real line. In these cases the analyticity properties result from the presence of the spectral parameter of the corresponding selfadjoint differential operator. Results in this paper are restricted to consideration of the classic Sturm-Liouville differential expression of the second-order, but under the minimal (locally Lebesgue integrable) conditions on the coefficients; furthermore the expression is taken to be in the regular and/or limit-circle end-point classification. This approach follows earlier work of Weiss, Kramer, Campbell and others, and recent results of Butzer, Zayed and Schottler. The new methods adopted here should extend to other end-point classifications and to symmetric differential expressions of arbitrary order. https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(1)/87-126.pdfsturm-liouvillelagrange interpolation |
| spellingShingle | W.N. EVERITT G. SCHOTTLER P.L. BUTZER Sturm-Liouville boundary value problems and Lagrange interpolation series Rendiconti di Matematica e delle Sue Applicazioni sturm-liouville lagrange interpolation |
| title | Sturm-Liouville boundary value problems and Lagrange interpolation series |
| title_full | Sturm-Liouville boundary value problems and Lagrange interpolation series |
| title_fullStr | Sturm-Liouville boundary value problems and Lagrange interpolation series |
| title_full_unstemmed | Sturm-Liouville boundary value problems and Lagrange interpolation series |
| title_short | Sturm-Liouville boundary value problems and Lagrange interpolation series |
| title_sort | sturm liouville boundary value problems and lagrange interpolation series |
| topic | sturm-liouville lagrange interpolation |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(1)/87-126.pdf |
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