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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 Relations between Limit-Point and Dirichlet Properties of Second-Order Difference Operators A. Delil | Hindawi Publishing Corporation Advances in Difference Equations Volume 2007 Article ID 94325 15 pages doi 10.1155 2007 94325 Research Article Relations between Limit-Point and Dirichlet Properties of Second-Order Difference Operators A. Delil Received 24 July 2006 Revised 6 March 2007 Accepted 11 April 2007 Dedicated to Professor W. D. Evans on the occasion of his 65th birthday Recommended by Martin J. Bohner We consider second-order difference expressions with complex coefficients of the form w 1 - A pn 1Axn 1 qnxn acting on infinite sequences. The discrete analog of some known relationships in the theory of differential operators such as Dirichlet conditional Dirichlet weak Dirichlet and strong limit-point is considered. Also connections and some relationships between these properties have been established. Copyright 2007 A. Delil. 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 In this paper we will deal with the second-order formally symmetric difference expression M acting on complex valued sequences x xn 1 defined by Mxn . A pn-1Axn-1 qnxn wn Axn w-1 n 0 n 1 1.1 with complex coefficients p pn 1 q q ĩ and weight w wn 1. In differential operators case when the coefficients p and q are real-valued the terms limit-point LP strong limit-point SLP Dirichlet D conditional Dirichlet CD and weak Dirichlet WD at the regular endpoint are often used to describe certain properties associated with the differential expression under consideration see 1-10 . Here we introduce the discrete analogue of these properties and some relations between them. In studying inequalities involving expression 1.1 such as HELP after Hardy Everitt Littlewood and Polya and Kolmogorov-type inequalities these properties and the relationships between 2 Advances in Difference Equations them are crucial. The work we .