scholarly journals On the fine spectrum of the second order difference operator over the sequence spaces ℓp and bvp,(1<p<∞)

2012 ◽  
Vol 55 (3-4) ◽  
pp. 426-431 ◽  
Author(s):  
Vatan Karakaya ◽  
Manaf Dzh. Manafov ◽  
Necip Şi̇mşek
Keyword(s):  
Difference Operator ◽  
Second Order ◽  
Sequence Spaces ◽  
Order Difference ◽  
Fine Spectrum

scholarly journals On the spectrum of 2-nd order generalized difference operator $\delta^2$ over the sequence space $c_0$

2013 ◽  
Vol 31 (2) ◽  
pp. 235 ◽  
Author(s):  
S. Dutta ◽  
Pinakadhar Baliarsingh
Keyword(s):  
Sequence Space ◽  
Difference Operator ◽  
Second Order ◽  
Order Difference ◽  
Fine Spectrum

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.

scholarly journals Spectrum and fine spectrum of generalized second order forward difference operator Δuvw2 $\Delta _{uvw}^2 $ on sequence space l1

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
B. L. Panigrahi ◽  
P. D. Srivastava
Keyword(s):  
Sequence Space ◽  
Difference Operator ◽  
Second Order ◽  
Fine Spectrum ◽  
Forward Difference

AbstractThe purpose of this paper is to determine spectrum and fine spectrum of newly introduced operator

scholarly journals On the fine spectrum of the generalized difference operatorB(r,s)over the sequence spacesc0andc

2005 ◽  
Vol 2005 (18) ◽  
pp. 3005-3013 ◽  
Author(s):  
Bilâl Altay ◽  
Feyzı Başar
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference ◽  
The Right

We determine the fine spectrum of the generalized difference operatorB(r,s)defined by a band matrix over the sequence spacesc0andc, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operatorΔ, and includes as other special cases the right shift and the Zweier matrices.

On difference sequence spaces of fractional-order involving Padovan numbers

2020 ◽  
pp. 2150095
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Syed Abdul Mohiuddine
Keyword(s):  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Hausdorff Measure Of Noncompactness ◽  
Order Difference ◽  
Matrix Formula ◽  
Difference Sequence Spaces

In this paper, we introduce Padovan difference sequence spaces of fractional-order [Formula: see text] [Formula: see text] [Formula: see text] by the composition of the fractional-order difference operator [Formula: see text] and the Padovan matrix [Formula: see text] defined by [Formula: see text] and [Formula: see text] respectively, where the sequence [Formula: see text] is the Padovan sequence. We give some topological properties, Schauder basis and [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the newly defined spaces. We characterize certain matrix classes related to the [Formula: see text] space. Finally, we characterize certain classes of compact operators on [Formula: see text] using Hausdorff measure of noncompactness.

scholarly journals Some Spectral Aspects of the Operator over the Sequence Spaces and

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Dutta ◽  
P. Baliarsingh
Keyword(s):  
Difference Operator ◽  
Main Idea ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Positive Real ◽  
Residual Spectrum ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference

The main idea of the present paper is to compute the spectrum and the fine spectrum of the generalized difference operator over the sequence spaces . The operator denotes a triangular sequential band matrix defined by with for , where or , ; the set nonnegative integers and is either a constant or strictly decreasing sequence of positive real numbers satisfying certain conditions. Finally, we obtain the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of the operator over the sequence spaces and . These results are more general and comprehensive than the spectrum of the difference operators , , , , and and include some other special cases such as the spectrum of the operators , , and over the sequence spaces or .

scholarly journals Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ruyun Ma ◽  
Chenghua Gao
Keyword(s):  
Eigenvalue Problems ◽  
Difference Operator ◽  
Second Order ◽  
Order Difference ◽  
Sign Changing Solutions

LetT>1be an integer, and let𝕋=1,2,…,T. We discuss the spectrum of discrete linear second-order eigenvalue problemsΔ2ut-1+λmtut=0, t∈𝕋,  u0=uT+1=0, whereλ≠0is a parameter,m:𝕋→ℝchanges sign andmt≠0on𝕋. At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.

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