|
Lecturer(s)
|
-
Staněk Svatoslav, prof. RNDr. CSc.
|
|
Course content
|
Functional Analysis Functional spaces. Basic principles of linear functional analysis. Operators (continuous, linear, compact, completely continuous, adjoint, closed). Spectral theory for linear operators. Fixed point theorems (Schauder and its corollaries, theorems based on degree of mapping, theorems in ordered spaces). Convex Analysis Convex sets and functionals. Kernel of convex set and the Minkowskii functional. Convex optimization. Duality in convex programming. Generalized convexity.
|
|
Learning activities and teaching methods
|
|
Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
|
|
Learning outcomes
|
Understand the theory of linear and nonlinear operators in functional spaces and the basic principles of convex analysis
Comprehension Understand the theory of linear and nonlinear operators in functional spaces and the basic principles of convex analysis.
|
|
Prerequisites
|
Master's degree in mathematics.
|
|
Assessment methods and criteria
|
Oral exam
Exam: to know and to understand the subject
|
|
Recommended literature
|
-
A. E. Taylor. (1977). Funkcionální analýza. Academia Praha.
-
Conway, J. B. (1990). A course in functional analysis. Springer.
-
J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
-
J.-B. Hiriart-Urruty, C. Lemaréchal. (1993). Convex analysis and minimization algorithms I, II. Springer Verlag, Berlin.
-
K. Deimling. (1985). Nonlinear functional analysis. Springer.
-
K. Najzar. (1988). Funkcionální analýza. SPN, Praha.
-
S. Fučík, A. Kufner. (1978). Nelineární diferenciální rovnice. SNTL Praha.
|