On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space
The representation of Nevanlinna Pick Problem is well known, see [7], [8] and [11]. The aim of this paper is to find the necessary and sufficient condition for the solution of Nevanlinna Pick Problem and to show that there is a one-to-one correspondence between the solutions of the Nevanlinna Pick P...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000628 |
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| _version_ | 1832562930269290496 |
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| author | A. A. El-Sabbagh |
| author_facet | A. A. El-Sabbagh |
| author_sort | A. A. El-Sabbagh |
| collection | DOAJ |
| description | The representation of Nevanlinna Pick Problem is well known, see [7], [8] and [11].
The aim of this paper is to find the necessary and sufficient condition for the solution of Nevanlinna
Pick Problem and to show that there is a one-to-one correspondence between the solutions of the
Nevanlinna Pick Problem and the minimal selfadjoint extensions of symmetric linear relation in
Hilbert space. Finally, we define the resolvent matrix which gives the solutions of the Nevanlinna
Pick Problem. |
| format | Article |
| id | doaj-art-1d998476b79a43a0bd2f06ebb30bc70a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1d998476b79a43a0bd2f06ebb30bc70a2025-02-03T01:21:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120345746410.1155/S0161171297000628On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert spaceA. A. El-Sabbagh0Department of Mathematics, Faculty of Engineering, Zagazig University, Shoubra, 108 Shoubra Street, Cairo, EgyptThe representation of Nevanlinna Pick Problem is well known, see [7], [8] and [11]. The aim of this paper is to find the necessary and sufficient condition for the solution of Nevanlinna Pick Problem and to show that there is a one-to-one correspondence between the solutions of the Nevanlinna Pick Problem and the minimal selfadjoint extensions of symmetric linear relation in Hilbert space. Finally, we define the resolvent matrix which gives the solutions of the Nevanlinna Pick Problem.http://dx.doi.org/10.1155/S0161171297000628Hilbert spaceoperatorssymmetric linear relationscompressed resolventselfadjont extensions and Nevanlinna pick problem. |
| spellingShingle | A. A. El-Sabbagh On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space International Journal of Mathematics and Mathematical Sciences Hilbert space operators symmetric linear relations compressed resolvent selfadjont extensions and Nevanlinna pick problem. |
| title | On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space |
| title_full | On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space |
| title_fullStr | On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space |
| title_full_unstemmed | On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space |
| title_short | On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space |
| title_sort | on the solution of nevanlinna pick problem with selfadjoint extensions of symmetric linear relations in hilbert space |
| topic | Hilbert space operators symmetric linear relations compressed resolvent selfadjont extensions and Nevanlinna pick problem. |
| url | http://dx.doi.org/10.1155/S0161171297000628 |
| work_keys_str_mv | AT aaelsabbagh onthesolutionofnevanlinnapickproblemwithselfadjointextensionsofsymmetriclinearrelationsinhilbertspace |