Sharp estimates for biorthogonal families to exponential functions associated to complex sequences without gap conditions
The general goal of this work is to obtain upper and lower bounds for the -norm of biorthogonal families to complex exponential functions associated to sequences which satisfy appropriate assumptions but without imposing a gap condition on the elements of the sequence. As a consequence, we also pres...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/153806 |
| Acesso em linha: | https://hdl.handle.net/11441/153806 https://doi.org/10.3934/eect.2023044 |
| Access Level: | acceso abierto |
| Palavra-chave: | Non scalar parabolic systems null controllability moment problem biorthogonal families no gap conditions control cost |
| Resumo: | The general goal of this work is to obtain upper and lower bounds for the -norm of biorthogonal families to complex exponential functions associated to sequences which satisfy appropriate assumptions but without imposing a gap condition on the elements of the sequence. As a consequence, we also present new results on the cost of the boundary null controllability of two parabolic systems at time : a phase-field system and a parabolic system whose generator has eigenvalues that accumulate. In the latter case, the behavior of the control cost when goes to zero depends strongly on the accumulation parameter of the eigenvalue sequence. |
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