TAILIEUCHUNG - Báo cáo hóa học: " Research Article On the Connection between Kronecker and Hadamard Convolution Products of Matrices and Some Applications"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Connection between Kronecker and Hadamard Convolution Products of Matrices and Some Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 736243 10 pages doi 2009 736243 Research Article On the Connection between Kronecker and Hadamard Convolution Products of Matrices and Some Applications Adem Kilicman1 and Zeyad Al Zhour2 1 Department of Mathematics Institute for Mathematical Research University Putra Malaysia 43400 UPM Serdang Selangor Malaysia 2 Department of Mathematics Zarqa Private University . Box 2000 Zarqa 1311 Jordan Correspondence should be addressed to Adem Kilicman akilicman@ Received 16 April 2009 Revised 29 June 2009 Accepted 14 July 2009 Recommended by Martin J. Bohner We are concerned with Kronecker and Hadamard convolution products and present some important connections between these two products. Further we establish some attractive inequalities for Hadamard convolution product. It is also proved that the results can be extended to the finite number of matrices and some basic properties of matrix convolution products are also derived. Copyright 2009 A. Kilicman and Z. Al Zhour. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction There has been renewed interest in the Convolution Product of matrix functions that is very useful in some applications see for example 1-6 . The importance of this product stems from the fact that it arises naturally in divers areas of mathematics. In fact the convolution product plays very important role in system theory control theory stability theory and other fields of pure and applied mathematics. Further the technique has been successfully applied in various fields of matrix algebra such as in matrix equations matrix differential equations matrix inequalities and many other subjects for details see 1 7 8 . For example in 2 Nikolaos established some .

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