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 $...
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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 |
| _version_ | 1818143294341775360 |
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| author | S. Dutta Pinakadhar Baliarsingh |
| author_facet | S. Dutta Pinakadhar Baliarsingh |
| author_sort | S. Dutta |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T11:29:23Z |
| format | Article |
| id | doaj.art-47da914fb7254545b4a396fff6f9a47c |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-11T11:29:23Z |
| publishDate | 2013-12-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-47da914fb7254545b4a396fff6f9a47c2022-12-22T01:08:54ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882013-12-0131223524410.5269/bspm.v31i2.175418659On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$S. Dutta0Pinakadhar Baliarsingh1Utkal University Department of MathematicsTrident Academy of Technology Department of MathematicsThe 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.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/17541Second order Difference operatorSpectrum of an operatorSequence spaces |
| spellingShingle | S. Dutta Pinakadhar Baliarsingh On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$ Boletim da Sociedade Paranaense de Matemática Second order Difference operator Spectrum of an operator Sequence spaces |
| title | On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$ |
| title_full | On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$ |
| title_fullStr | On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$ |
| title_full_unstemmed | On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$ |
| title_short | On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$ |
| title_sort | on the spectrum of 2 nd order generalized difference operator delta 2 over the sequence space c 0 |
| topic | Second order Difference operator Spectrum of an operator Sequence spaces |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/17541 |
| work_keys_str_mv | AT sdutta onthespectrumof2ndordergeneralizeddifferenceoperatordelta2overthesequencespacec0 AT pinakadharbaliarsingh onthespectrumof2ndordergeneralizeddifferenceoperatordelta2overthesequencespacec0 |