Spectral analysis of second order quantum difference operator over the sequence space lp (1 < p < ∞)

Authors

DOI:

https://doi.org/10.31489/2025m2/122-136

Keywords:

spectrum, difference operator, infinite matrices, triple-band matrix

Abstract

In this article, we study the spectrum, fine spectrum and boundedness property of second order quantum difference operator ∆2q (0 < q < 1) over the class of sequence lp (1 < p < ∞), the pth summable sequence space. The second order quantum difference operator ∆2q is a lower triangular triple band matrix ∆2q(1,−(1+ q),q). We also determine the approximate point spectrum, defect spectrum, compression spectrum, and Goldberg classification of the operator on the class of sequence. We obtained the results by solving an infinite system of linear equations and computing the inverse of a lower triangular infinite matrix. We also provide appropriate examples along with graphical representations where necessary.

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Published

2025-06-30

How to Cite

Kalita, N., & Dutta, A. (2025). Spectral analysis of second order quantum difference operator over the sequence space lp (1 < p < ∞). Bulletin of the Karaganda University. Mathematics Series, 118(2), 122–136. https://doi.org/10.31489/2025m2/122-136

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Section

MATHEMATICS