Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910050859089920 |
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| author | Baustian, Falko Bobkov, Vladimir |
| author_facet | Baustian, Falko Bobkov, Vladimir |
| contents | We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,π)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fucik eigenvalues which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,π)$ and we explicitly describe the corresponding biorthogonal system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06244 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian Baustian, Falko Bobkov, Vladimir Classical Analysis and ODEs Analysis of PDEs Spectral Theory 34L10, 34B08, 47A70 We investigate the basis properties of sequences of Fucik eigenfunctions of the one-dimensional Neumann Laplacian. We show that any such sequence is complete in $L^2(0,π)$ and a Riesz basis in the subspace of functions with zero mean. Moreover, we provide sufficient assumptions on Fucik eigenvalues which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in $L^2(0,π)$ and we explicitly describe the corresponding biorthogonal system. |
| title | Basisness and completeness of Fucik eigenfunctions for the Neumann Laplacian |
| topic | Classical Analysis and ODEs Analysis of PDEs Spectral Theory 34L10, 34B08, 47A70 |
| url | https://arxiv.org/abs/2204.06244 |