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Course, academic year 2019/2020
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Differentiability of functions in Banach spaces I - NRFA183
Title in English: Diferencovatelnost funkcí v Banachových prostorech I
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: both
E-Credits: 3
Hours per week, examination: 2/0 C [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Note: you can enroll for the course in winter and in summer semester
Class: DS, matematická analýza
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Annotation -
Last update: T_KMA (09.05.2012)
The lecture will concentrate on some aspects of geometrical nonlinear analysis, in which the lecturer works. For example, differentiability (of the first degree) of convex and Lipschitz functions and the corresponding classes of exceptional sets will be studied. Several open questions will be mentioned.
Syllabus -
Last update: T_KMA (09.05.2012)

Some basic types of derivatives (Fréchet, strict, Gâteaux, Hadamard), directional derivatives,

subdifferentials (Clarke, Fréchet). Fréchet and Gâteaux differentiability of convex and Lipschitz functions (and semiconvex functions). Systems of exceptional sets (sigma-porous sets, Aronszajn null sets, Gamma-null sets). Applications to DC functions and mappings and applications in abstract approximation theory.

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