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Non-archimedean linear operators and applications /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hauppauge, N.Y. : Lancaster :
Nova Science ; Gazelle [distributor],
2009.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- NON-ARCHIMEDEAN LINEAR OPERATORSAND APPLICATIONS; Contents; Preface; Non-Archimedean Valued Fields; 1.1 Introduction; 1.2 Non-Archimedean Valued Fields; 1.2.1 Basic Definitions; 1.2.2 The t-Vector Space Kt; 1.3 Construction of Qp; 1.3.1 Introduction; 1.3.2 The Field Qp; 1.3.3 Convergence of Power Series overQp; 1.4 Construction of K((x)); 1.5 Bibliographical Notes; Non-Archimedean Banach and HilbertSpaces; 2.1 Non-Archimedean Banach Spaces; 2.1.1 Basic Definitions; 2.1.2 Examples of Non-Archimedean Banach Spaces; 2.2 Free Banach Spaces; 2.2.1 Definitions; 2.2.2 Examples.
- 2.3 Non-Archimedean Hilbert Spaces2.3.1 Introduction; 2.3.2 Non-Archimedean Hilbert Spaces; 2.3.3 The Hilbert Space Ew1 Ew2 ... Ewt; 2.4 Bibliographical Notes; Non-Archimedean Bounded LinearOperators; 3.1 Introduction; 3.2 Bounded Linear Operators on Non-Archimedean Banach Spaces; 3.2.1 Basic Definitions; 3.2.2 Examples; 3.2.3 The Banach Algebra B(X); 3.2.4 Further Properties of Bounded Linear Operators; 3.3 Bounded Linear Operators on Hilbert Spaces Ew; 3.3.1 Introduction; 3.3.2 Representation of Bounded Operators By Infinite Matrices; 3.3.3 Existence of the Adjoint.
- 3.3.4 Examples of Bounded Operators with no Adjoint3.4 Perturbation of Bases; 3.5 Hilbert-Schmidt Operators; 3.5.1 Basic Definitions; 3.5.2 Further Properties of Hilbert-Schmidt Operators; 3.5.3 Completely Continuous Operators; 3.5.4 Trace; 3.5.5 Examples; 3.6 Open Problems; 3.7 Bibliographical Notes; Non-Archimedean Unbounded LinearOperators; 4.1 Introduction; 4.2 Basic Definitions; 4.2.1 Example; 4.2.2 Existence of the Adjoint; 4.2.3 Examples of Unbounded Operators With no Adjoint; 4.3 Closed Linear Operators on Ew; 4.4 Diagonal Operators on Ew; 4.5 Open Problems; 4.6 Bibliographical Notes.
- Non-Archimedean Bilinear Forms5.1 Introduction; 5.2 Basic Definitions; 5.2.1 Continuous Linear Functionals on Ew; 5.2.2 Bounded Bilinear Forms on Ew Ew; 5.2.3 Unbounded Bilinear Forms on Ew Ew; 5.3 Closed and Closable non-Archimedean Bilinear Forms; 5.3.1 Closedness of the Form Sum; 5.3.2 Construction of a non-Archimedean Hilbert Space Using Quadratic Forms; 5.3.3 Further Properties of the Closure; 5.4 Representation of Bilinear Forms on Ew Ew by Linear Operators; 5.5 Bibliographical Notes; Functions of Some Self-adjoint LinearOperators on Ew; 6.1 Introduction.
- 6.2 Products and Sums of Diagonal Operators6.3 Integer Powers of Diagonal Operators; 6.4 Functions of Self-Adjoint Operators; 6.5 Functions of Some Symmetric Square Matrices Over Qp Qp; 6.5.1 The Powers of the Matrix T; 6.5.2 Exponential of the Matrix T; 6.6 Open Problems; 6.7 Bibliographical Notes; One-Parameter Family of Bounded LinearOperators on Free Banach Spaces; 7.1 Introduction; 7.2 Basic Definitions; 7.3 Properties of non-Archimedean C0-Groups; 7.4 Existence of Solutions to Some p-adic Differential Equations; 7.5 Open Problems; 7.6 Bibliographical Notes; References; Index.