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Banach spaces. --- Differential equations, Linear. --- Integral equations. --- Operator equations.
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Introduction to Banach spaces and their geometry
Espaces linéaires normés. --- Normed linear spaces --- Banach spaces. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Functions of complex variables --- Generalized spaces --- Topology --- Normed linear spaces. --- Espaces de banach
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Analytical spaces --- 517.5 --- Theory of functions --- Banach spaces. --- Functions, Continuous. --- Schauder bases. --- 517.5 Theory of functions --- Bases (Linear topological spaces) --- Bases (espaces vectoriels topologiques) --- Banach, Espaces de. --- Fonctions continues --- Functions, Continuous
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Analytical spaces --- Harmonic analysis. Fourier analysis --- Stochastic processes --- Mathematical potential theory --- Banach spaces --- Harmonic analysis --- Martingales (Mathematics) --- Congresses. --- Processus stochastiques --- Probabilités. --- Probabilities --- Probabilities. --- Stochastic processes. --- Probabilités --- Theorie du potentiel
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In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis.
Banach algebras. --- Semigroups. --- Group theory --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Banach algebras --- Semigroups --- Banach, Algèbres de --- Semi-groupes --- Ordered algebraic structures --- Analytical spaces
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System theory
Mathematical control systems --- System Analysis --- System analysis. --- Analyse de systèmes --- Hilbert space --- Espace de Hilbert --- System analysis --- 517.982 --- 517.983 --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.983 Linear operators. Linear operator equations --- Linear operators. Linear operator equations --- 517.982 Linear spaces with topology and order or other structures --- Linear spaces with topology and order or other structures --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Banach spaces --- Hyperspace --- Inner product spaces --- Hilbert space.
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