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.
@article{17541,
title = {On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c\_0$},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {31},
year = {2013},
doi = {10.5269/bspm.v31i2.17541},
language = {EN},
url = {http://dml.mathdoc.fr/item/17541}
}
Dutta, S.; Baliarsingh, Pinakadhar. On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$. Boletim da Sociedade Paranaense de Matemática, Tome 31 (2013) . doi : 10.5269/bspm.v31i2.17541. http://gdmltest.u-ga.fr/item/17541/