Contribution to the study of operators in sequence spaces and applications to optimization and differential systems
Identifieur interne : 000A99 ( Main/Exploration ); précédent : 000A98; suivant : 000B00Contribution to the study of operators in sequence spaces and applications to optimization and differential systems
Auteurs : Ali Fares [France]Source :
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Abstract
In this thesis we deal with linear operators between sequence spaces. We are led to studying matrix transformations and solving linear systems of infinitely many equations in infinitely many unknowns. We give some applications to solving differential systems involving special matrices. Then we are interested in solving sequence space equations (SSE), which are identities in which each term is a sum or product of sets of sequences of the form s_a and s_{\phi(x)} where \phi is a map from U^+ into itself and x is the unknown sequence. Solving such equations is equivalent to determining the set of all sequences x which satisfy the equation. Then, we study the spectrum of the operator of the first difference \Delta in the new sequences spaces s_a, s_a^0, s_a^{(c)} and l_p (a) where 1\leq p < \infty. Finally we consider direct applications of the theory of infinite matrices in optimization problems where we present some results given by B. of Malafosse and A. Yassine to determine the number of ways having N arcs and connecting any two points in the plane with an infinite Boolean Toeplitz matrix.
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We are led to studying matrix transformations and solving linear systems of infinitely many equations in infinitely many unknowns. We give some applications to solving differential systems involving special matrices. Then we are interested in solving sequence space equations (SSE), which are identities in which each term is a sum or product of sets of sequences of the form s_a and s_{\phi(x)} where \phi is a map from U^+ into itself and x is the unknown sequence. Solving such equations is equivalent to determining the set of all sequences x which satisfy the equation. Then, we study the spectrum of the operator of the first difference \Delta in the new sequences spaces s_a, s_a^0, s_a^{(c)} and l_p (a) where 1\leq p < \infty. Finally we consider direct applications of the theory of infinite matrices in optimization problems where we present some results given by B. of Malafosse and A. Yassine to determine the number of ways having N arcs and connecting any two points in the plane with an infinite Boolean Toeplitz matrix.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Haute-Normandie</li><li>Région Normandie</li></region><settlement><li>Le Havre</li></settlement><orgName><li>Université du Havre</li></orgName></list><tree><country name="France"><region name="Région Normandie"><name sortKey="Fares, Ali" sort="Fares, Ali" uniqKey="Fares A" first="Ali" last="Fares">Ali Fares</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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