Some Spectral Aspects of the Operator Δνr over the Sequence Spaces ℓp and bvp (1
Joint Authors
Source
Chinese Journal of Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-07
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The main idea of the present paper is to compute the spectrum and the fine spectrum of the generalized difference operator Δνr over the sequence spaces bvp (1
The operator Δνr denotes a triangular sequential band matrix (ank) defined by Δνr(x)=(Δνrx)k=∑i=0r(-1)i(ri)νk-ixk-i, with xk=νk=0 for k<0, where x∈ℓp or bvp, r,k∈ℕ0={0,1,2,3,...}; the set nonnegative integers and ν=(νk) 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 Δνr over the sequence spaces ℓp and bvp.
These results are more general and comprehensive than the spectrum of the difference operators Δ, Δν, Δ2, Δuv2, and Δr and include some other special cases such as the spectrum of the operators B(r,s), B(r,s,t), and Δab over the sequence spaces ℓp or bvp (1
American Psychological Association (APA)
Dutta, S.& Baliarsingh, P.. 2013. Some Spectral Aspects of the Operator Δνr over the Sequence Spaces ℓp and bvp (1
Chinese Journal of Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-460498
Modern Language Association (MLA)
Dutta, S.& Baliarsingh, P.. Some Spectral Aspects of the Operator Δνr over the Sequence Spaces ℓp and bvp (1
Chinese Journal of Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-460498
American Medical Association (AMA)
Dutta, S.& Baliarsingh, P.. Some Spectral Aspects of the Operator Δνr over the Sequence Spaces ℓp and bvp (1
Chinese Journal of Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-460498
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460498