On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$
The main purpose of this article is to determine the spectrum and the fine spectrum of second order difference operator $\Delta^2$ over the sequence space $c_0$. For any sequence $(x_k)_0^\infty$ in $c_0$, the generalized second order difference operator $\Delta^2$ over $c_0$ is defined by $...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2013-12-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/17541 |
| Summary: | The main purpose of this article is to determine the spectrum and the fine spectrum of second order difference operator $\Delta^2$ over the sequence space $c_0$. For any sequence $(x_k)_0^\infty$ in $c_0$, the generalized second order difference operator $\Delta^2$ over $c_0$ is defined by $\Delta^2(x_k)= \sum_{i=0}^2(-1)^i\binom{2}{i}x_{k-i}=x_k-2x_{k-1}+x_{k-2}$, with $ x_{n} = 0$ for $n<0$.Throughout we use the convention that a term with a negative subscript is equal to zero. |
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| ISSN: | 0037-8712 2175-1188 |