Found 6 relevant results in 1.99s where lecturer="Alessandro Carlotto"
Banach and Hilbert spaces, bounded linear operators; Hahn Banach, Baire Category, Uniform boundedness and Banach Steinhaus Theorem, open mapping/closed graph theorem; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; Uniformly Convex Spaces; Application to L^p Spaces; Compact operators, Spectral theory of self-adjoint compact operators. Sobolev spaces.
The course will focus on the study of fundamental functional analysis methods relevant to the analysis of Partial Differential Equations and harmonic analysis.
Mathematics III: Partial Differential Equations
Mathematik III: Partielle Differentialgleichungen
Examples of partial differential equations. Linear partial differential equations. Separation of variables. Fourier series, Fourier transform, Laplace transform. Applications to solving commonly encountered linear partial differential equations (Laplace's Equation, Heat Equation, Wave Equation).
This course is meant as an invitation to some key ideas and techniques in Geometric Analysis, with special emphasis on the theory of minimal surfaces. It is primarily conceived for advanced Bachelor or beginning Master students.
Topics covered include: topological spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.
Topics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.