Hereditary completeness of Exponential systems $\{e^{λ_n t}\}_{n=1}^{\infty}$ in their closed span in $L^2 (a, b)$ and Spectral Synthesis
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913182902124544 |
|---|---|
| author | Zikkos, Elias Gunatillake, Gajath |
| author_facet | Zikkos, Elias Gunatillake, Gajath |
| contents | Suppose that $\{λ_n\}_{n=1}^{\infty}$ is a sequence of distinct positive real numbers satisfying the conditions inf$\{λ_{n+1}-λ_n \}>0,$ and $\sum_{n=1}^{\infty}λ_n^{-1}<\infty.$ We prove that the exponential system $\{e^{λ_n t}\}_{n=1}^{\infty}$ is hereditarily complete in the closure of the subspace spanned by $\{e^{λ_n t}\}_{n=1}^{\infty}$ in the space $L^2 (a,b)$. We also give an example of a class of compact non-normal operators defined on this closure which admit spectral synthesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hereditary completeness of Exponential systems $\{e^{λ_n t}\}_{n=1}^{\infty}$ in their closed span in $L^2 (a, b)$ and Spectral Synthesis Zikkos, Elias Gunatillake, Gajath Functional Analysis Classical Analysis and ODEs Complex Variables 30B60, 30B50, 47A10, 46C05 Suppose that $\{λ_n\}_{n=1}^{\infty}$ is a sequence of distinct positive real numbers satisfying the conditions inf$\{λ_{n+1}-λ_n \}>0,$ and $\sum_{n=1}^{\infty}λ_n^{-1}<\infty.$ We prove that the exponential system $\{e^{λ_n t}\}_{n=1}^{\infty}$ is hereditarily complete in the closure of the subspace spanned by $\{e^{λ_n t}\}_{n=1}^{\infty}$ in the space $L^2 (a,b)$. We also give an example of a class of compact non-normal operators defined on this closure which admit spectral synthesis. |
| title | Hereditary completeness of Exponential systems $\{e^{λ_n t}\}_{n=1}^{\infty}$ in their closed span in $L^2 (a, b)$ and Spectral Synthesis |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables 30B60, 30B50, 47A10, 46C05 |
| url | https://arxiv.org/abs/2401.01132 |