Fundamentals of Advanced Mathematics 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves

Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. Present Galois Theory, transcendental field extensions, and PicardIncludes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations INDICE: 1. Field and differential field extensions1.1 Galois theory1.2 Transcendental field extensions1.3 Differential Galois theory (Picard-Vessiot)1.4 Differentially transcendental field extensions2. Topology and topological vector spaces2.1 General topology2.2 Topological vector spaces2.2.1 General theory2.2.2 Locally convex spaces2.2.3 Duality2.2.4 Spaces of linear continuous mappings2.2.5 Hilbert spaces3. Differential and integral calculus3.1 Radon measures3.2 Differential calculus in Banach spaces4. Sheaves4.1 General theory4.2 Sheaves of Modules4.3 Sheaves of distributions4.4 Sheaves of hyperfunctions4.5 Application to algebraic analysis (local theory of systems of linear differential equations with time-varying coefficients)

• ISBN: 978-1-78548-249-6
• Editorial: ISTE Press - Elsevier
• Encuadernacion: Cartoné
• Páginas: 230
• Fecha Publicación: 01/12/2017
• Nº Volúmenes: 1
• Idioma: Inglés