Course Unit

Catalogue

Applications of the theory of functional equations

Unit Coordinator: Roman Ger
Programme: Double Degrees
ECTS Credits: 6
Semester: 2
Year: 2
Campus: University of Silesia in Katowice
Language: English
Content:
  • Applications in Geometry:

             1. Joint characterization of Euclidean, hyperbolic and elliptic geometries.

             2. Characterizations of the cross ratio.

             3. A description of certain subsemigroups of some Lie groups.

  • Applications in Functional Analysis:

    1. Analytic form of linear-multiplicative functionals in the Banach algebra of integrable functions on the real line.

    2. A characterization of strictly convex spaces.

    3. Some new characterizations of inner product spaces.

    4. Birkhoff-James orthogonality.

    5. Addition theorems in Banach algebras; operator semigroups.

Reading list:

1. J. Aczel & J. Dhombres, Functional equations in several variables, Cambridge University Press, Cambridge, 1989.

2. J. Aczel & S. Gołąb, Funktionalgleichungen der Theorie der Geometrischen Objekte, PWN, Warszawa, 1960.

3. J. Dhombres, Some aspects of functional equations, Chulalongkorn Univ., Bangkok, 1979.

4. D. Ilse, I. Lehman and W. Schulz, Gruppoide und Funktionalgleichungen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1984.

5. M. Kuczma, An introduction to the theory of functional equations and inequalities, Polish ScientiSc Publishers & Silesian University, Warszawa-Kraków-Katowice, 1985.


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