Analytic Kramer sampling and quasi Lagrange-type interpolation in vector valued RKHS
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| Format: | Preprint |
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2024
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| _version_ | 1866913477085364224 |
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| author | Mahapatra, Subhankar Sarkar, Santanu |
| author_facet | Mahapatra, Subhankar Sarkar, Santanu |
| contents | This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for functions within a RKHS of vector valued entire functions. The dependence of having quasi Lagrange-type interpolation on an invariance condition under the generalized backward shift operator has also been discussed. Furthermore, the paper establishes the connection between quasi Lagrange-type interpolation, operator of multiplication by the independent variable, and de Branges spaces of vector valued entire functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_20317 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic Kramer sampling and quasi Lagrange-type interpolation in vector valued RKHS Mahapatra, Subhankar Sarkar, Santanu Functional Analysis Primary: 46E22, 46E40, Secondary: 47B32, 94A20 This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for functions within a RKHS of vector valued entire functions. The dependence of having quasi Lagrange-type interpolation on an invariance condition under the generalized backward shift operator has also been discussed. Furthermore, the paper establishes the connection between quasi Lagrange-type interpolation, operator of multiplication by the independent variable, and de Branges spaces of vector valued entire functions. |
| title | Analytic Kramer sampling and quasi Lagrange-type interpolation in vector valued RKHS |
| topic | Functional Analysis Primary: 46E22, 46E40, Secondary: 47B32, 94A20 |
| url | https://arxiv.org/abs/2405.20317 |