| Titre : |
Problems associated with linear differential equations |
| Type de document : |
texte imprimé |
| Auteurs : |
M. Ben Ammar, Auteur ; W. D. Evans, Directeur de thèse |
| Editeur : |
Pays de Galles : University of Wales |
| Année de publication : |
1988 |
| Importance : |
117 f. |
| Présentation : |
ill. |
| Format : |
27 cm. |
| Note générale : |
Mémoire de Magister : Mathématiques Pures: Royaume Uni, University of Wales : 1988
Bibliogr. f. 118 - 119 |
| Langues : |
Anglais (eng) |
| Mots-clés : |
Pure -- mathematics Minimal operators Maximal Linear differential equations |
| Index. décimale : |
M002388 |
| Résumé : |
In this thesis we study the spectral properties of operators which are generated by general first-order differential expressions of the form
τ = p(x) d/dx + q(x) in a weighted Hilbert space L²w(a,b).
Since solutions of related integral equations can be obtained explicitly, we are able to analyse in detail the properties of these operators and give a much more complete description than is possible for higher-order differential operators.
We are particularly concerned with expressions τ which are not formally symmetric, i.e., τ = τ⁺, where τ⁺ is the formal adjoint of τ and especially with the operators which are regularly solvable with respect to the minimal operators generated by τ and τ⁺ in the sense of W. D. Evans.
Chapter I is an introduction in which the problems studied in the thesis are introduced.
Also terms which will be used later are defined and results which are used often in the thesis are quoted.
Chapter II deals with the regular problem.
In II.1 there is some preliminary material on τ and τ⁺ and the conditions to be imposed on the coefficients are given and explained.
The minimal operators T₀(τ), T₀(τ⁺) generated by τ, τ⁺ respectively are studied in detail in II.2.
Operators S which are regularly solvable with respect to T₀(τ), T₀(τ⁺) are shown to be characterized by boundary conditions at the end points of [a,b], the eigenvalues and eigenvectors of S and its adjoint S* are found and their resolvents are constructed and discussed.
The singular problem is discussed in chapter III and results analogous to those in chapter II are obtained.
Particular attention is paid to the fields of regularity of T₀(τ) and T₀(τ⁺) in this case. |
Problems associated with linear differential equations [texte imprimé] / M. Ben Ammar, Auteur ; W. D. Evans, Directeur de thèse . - Pays de Galles : University of Wales, 1988 . - 117 f. : ill. ; 27 cm. Mémoire de Magister : Mathématiques Pures: Royaume Uni, University of Wales : 1988
Bibliogr. f. 118 - 119 Langues : Anglais ( eng)
| Mots-clés : |
Pure -- mathematics Minimal operators Maximal Linear differential equations |
| Index. décimale : |
M002388 |
| Résumé : |
In this thesis we study the spectral properties of operators which are generated by general first-order differential expressions of the form
τ = p(x) d/dx + q(x) in a weighted Hilbert space L²w(a,b).
Since solutions of related integral equations can be obtained explicitly, we are able to analyse in detail the properties of these operators and give a much more complete description than is possible for higher-order differential operators.
We are particularly concerned with expressions τ which are not formally symmetric, i.e., τ = τ⁺, where τ⁺ is the formal adjoint of τ and especially with the operators which are regularly solvable with respect to the minimal operators generated by τ and τ⁺ in the sense of W. D. Evans.
Chapter I is an introduction in which the problems studied in the thesis are introduced.
Also terms which will be used later are defined and results which are used often in the thesis are quoted.
Chapter II deals with the regular problem.
In II.1 there is some preliminary material on τ and τ⁺ and the conditions to be imposed on the coefficients are given and explained.
The minimal operators T₀(τ), T₀(τ⁺) generated by τ, τ⁺ respectively are studied in detail in II.2.
Operators S which are regularly solvable with respect to T₀(τ), T₀(τ⁺) are shown to be characterized by boundary conditions at the end points of [a,b], the eigenvalues and eigenvectors of S and its adjoint S* are found and their resolvents are constructed and discussed.
The singular problem is discussed in chapter III and results analogous to those in chapter II are obtained.
Particular attention is paid to the fields of regularity of T₀(τ) and T₀(τ⁺) in this case. |
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