Applied functional analysis |
ter |
|||||
Teaching Staff in Charge |
Prof. COBZAS Stefan, Ph.D., scobzas@math.ubbcluj.ro |
Aims |
To present some results from the duality theory for locally convex spaces and from Banach space theory, which are most used in optimization and best approximation problems. |
Content |
Support functionals - Bishop-Phelps subreflexivity and James reflexivity theorems. Geometric properties of normed spaces -strict convexity, local uniform convexity and uniform convexity. Extremal points and support functionals of the unit balls in concrete Banach spaces. Differential and integral calculus in Banach spaces. Convex functions - continuity and differentiability. Smoothness properties of normed spaces - Gateaux and Frechet differentiability of the norm. Holomorphic vector functions - the equivalence of weak and strong holomorphy. |
References |
1. Holmes R.B., Geometric functional analysis, Springer Verlag, Berlin 1975.
2. Kantorovich L. V. si Akilov G.P., Analiza functionala, Editura Stiintifica si Enciclopedica, Bucuresti 1986. 3. S.S. Kutateladze, Fundamentals of functional analysis, Kluwer A. P. , Dordrecht 1995. 4. Muntean I., Analiza functionala, Litografiat Universitatea Babes-Bolyai, Cluj-Napoca 1993. 5. Muntean I., Analiza functionala-Capitole speciale, Litografiat Universitatea Babes -Bolyai, Cluj-Napoca 1990. 6. Rudin W., Functional analysis, McGraw Hill, New York 1973. 7. Schaeffer H.H., Topological vector spaces, MacMilan New York 1966. 7. Yosida K., Functional analysis, Springer Berlin 1965. |
Assessment |
Exam. |