optimal error of analytic continuation from a finite set with inaccurate data in hilbert spaces of holomorphic functions: Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions
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| Titel: | optimal error of analytic continuation from a finite set with inaccurate data in hilbert spaces of holomorphic functions: Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions |
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| Autoren: | L. S. Maergoiz, A. M. Fedotov |
| Quelle: | Siberian Mathematical Journal. 42(5):926-935 |
| Verlagsinformationen: | Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk, 2001. |
| Publikationsjahr: | 2001 |
| Schlagwörter: | analytic continuation, Entire functions of several complex variables, Removable singularities in several complex variables, Continuation of analytic objects in several complex variables, extrapolation with inaccurate data, optimal error, optimal linear algorithm |
| Beschreibung: | The article under review refers to the papers [\textit{L.~S.~Maergojz}, Sib. Math. J. 41, No. 6, 1126-1136 (2000; Zbl 0970.32011) and Dokl. Math. 56, No. 2, 674-678 (1997; Zbl 0973.32002)] wherein the problem of optimal extrapolation from a finite set is studied in the class of entire functions with finite spectrum. The aim of the present article is to study this problem in the case of analytic continuation from a finite set with inaccurate data. To estimate the error of a linear functional, an approach is employed suggested by \textit{K.~Miller} in [SIAM J. Math. Anal. 1, 52-74 (1970; Zbl 0214.14804)] based on using the least squares method for ill-posed problems with a prescribed bound. As a result, the authors obtain constructive formulas for calculating the optimal error of the optimal linear algorithm for extrapolation from a set \(U\) to a point \(z_0\) in the class of functions \[ V = \{f\in H(D): \|f\|\leq r\}, \quad r > 0, \] where \(H\) is a Hilbert space with reproducing kernel. Moreover, the asymptotic behavior of the optimal error is investigated in the case when the errors of estimating the initial data tend to zero. |
| Publikationsart: | Article |
| Dateibeschreibung: | application/xml |
| ISSN: | 0037-4466 |
| DOI: | 10.1023/a:1011967711386 |
| Zugangs-URL: | https://zbmath.org/1746519 https://link.springer.com/article/10.1023%2FA%3A1011967711386 |
| Dokumentencode: | edsair.dedup.wf.002..a40bceb4194ec2e42a7c72c4b51f7966 |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | The article under review refers to the papers [\textit{L.~S.~Maergojz}, Sib. Math. J. 41, No. 6, 1126-1136 (2000; Zbl 0970.32011) and Dokl. Math. 56, No. 2, 674-678 (1997; Zbl 0973.32002)] wherein the problem of optimal extrapolation from a finite set is studied in the class of entire functions with finite spectrum. The aim of the present article is to study this problem in the case of analytic continuation from a finite set with inaccurate data. To estimate the error of a linear functional, an approach is employed suggested by \textit{K.~Miller} in [SIAM J. Math. Anal. 1, 52-74 (1970; Zbl 0214.14804)] based on using the least squares method for ill-posed problems with a prescribed bound. As a result, the authors obtain constructive formulas for calculating the optimal error of the optimal linear algorithm for extrapolation from a set \(U\) to a point \(z_0\) in the class of functions \[ V = \{f\in H(D): \|f\|\leq r\}, \quad r > 0, \] where \(H\) is a Hilbert space with reproducing kernel. Moreover, the asymptotic behavior of the optimal error is investigated in the case when the errors of estimating the initial data tend to zero. |
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| ISSN: | 00374466 |
| DOI: | 10.1023/a:1011967711386 |