|
Lecturer(s)
|
-
Andres Jan, prof. RNDr. dr hab. DSc.
-
Tomeček Jan, doc. RNDr. Ph.D.
-
Vodák Rostislav, doc. RNDr. Ph.D.
|
|
Course content
|
Functional spaces. Basic principles of linear functional analysis. Operators (continuous, linear, compact, completely continuous, adjoint, closed). General forms of linear continuous functionls. Fredholm theorems. Spectral theory for linear operators. Fixed point theorems (Schauder and its corollaries, theorems based on degree of mapping). Derivative of operators. Basics of nonlinear analysis.
|
|
Learning activities and teaching methods
|
|
unspecified
|
|
Learning outcomes
|
Master methods and tools of linear functional analysis and tools of nonlinear functional analysis.
|
|
Prerequisites
|
unspecified
|
|
Assessment methods and criteria
|
unspecified
|
|
Recommended literature
|
-
Aktuální odborné články v mezinárodních matematických časopisech.
-
A. E. Taylor. (1977). Funkcionální analýza. Academia Praha.
-
A. Sasane. (2017). Friendly Approach To Functional Analysis. WSPC.
-
Conway, J. B. (1990). A course in functional analysis. Springer.
-
Dolejší, V., Najzar, K. (2010). Nelineární funkcionální analýza. MATFYZPRESS, Praha.
-
J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
-
K. Deimling. (1985). Nonlinear functional analysis. Springer.
-
M. Fabian a kol. (2001). Functional Analysis and Infinite-Dimensional Geometry. Springer, Berlin.
-
S. Fučík, A. Kufner. (1978). Nelineární diferenciální rovnice. SNTL Praha.
|