Murat Kirisci, Harun Polat

DOI Number
First page
Last page


In this paper, some applications of the Hilbert matrix in image processing and cryptology are mentioned and an algorithm related to the Hilbert view of a digital image is given. New matrix domains are constructed and some of their properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix transformations are characterized. Finally, examples of transformations of new spaces are given.


Hilbert matrix; cryptology; image processing; matrix domains.


Hilbert matrix, dierence operator, matrix domain, image processing, isomorphic copy.

Full Text:



B. Altay and F. Ba¸sar: Certain topological properties and duals of the domain of a triangle matrix in a sequence spaces, J. Math. Anal. Appl., 336 (2007), 632–645.

B. Altay, F. Ba¸sar and M. Mursaleen: On the Euler sequence spaces which include the spaces ℓp and ℓ∞ I, Inform. Sci. 176(10)(2006), 1450–1462.

B. Altay and F. Ba¸sar: On some Euler sequence spaces of non-absolute type, Ukrainian Math. J. 57(1)(2005), 1–17.

F. Ba¸sar and B. Altay: On the space of sequences of p-bounded variation and related matrix mappings, Ukranian Math. J., 55(1) (2003), 136–147.

M. D. Choi: Tricks or treats with the Hilbert Matrix, Amer. Math. Monthly 90, (1983), 301–312.

R. C¸ olak and M. Et: On some generalized difference sequence spaces and related matrix transformations, Hokkaido Math. J., 26(3), (1997), 483–492.

M. Et and R. C¸ olak: On some generalized difference sequence spaces, Soochow J. Math., 21(4), (1995), 377–386.

G. H. Hardy, J. E. Littlewood and G. Polya: Inequalities, Cambridge Univ.

Press, U.K., 1934.

E. E. Kara and M. Ilkhan: Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear Algebra, 39(2), (2016), 217–230, DOI:10.1080/03081087.2016.1145626.

M. Kiri¸sci: On the Taylor sequence spaces of nonabsolute type which include the spaces c0 and c, J. Math. Anal., 6(2), 22–35, (2015).

M. Kiri¸sci: The Application Domain of Infinite Matrices with Algorithms, Universal Journal of Mathematics and Applications , 1(1), 1–9, (2018).

H. Kızmaz: On certain sequence space, Can. Math. Bull. 24(2), (1981), 169–176.

Ng, P. N. and Lee, P. -Y.: Cesa`ro sequence spaces of non-absolute type, Comment.

Math. Prace Mat. 20(2), 429–433, (1978).

E. Malkowsky: Recent results in the theory of matrix transformations in sequence spaces, Mat. Ves. 49, 187–196, (1997).

Y. Matsuo: Matrix theory, Hilbert Scheme and Integrable system, Mod. Phys. Lett.

A, 13, (1998), http://dx.doi.org/10.1142/S0217732398002904

J. F. Peters: Topology of Digital Images, Intelligent Systems Reference Library, Volume 63, Springer, 2014.

H. Polat: Some new Hilbert sequence spaces, Mus Alparslan University Journal of Science, (2016).

P. V. K. Raja, A. S. N. Chakravarthy and P. S. Avadhani: A Cryptosystem based on Hilbert matrix using cipher block chaining mode, International Joournal of Mathematical Trends and Technology(IJMIT), 2(1), (2011), 17–22.

DOI: https://doi.org/10.22190/FUMI1902359K


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)