Powers of topological groups characters and a theorem of van der Corput

• Autorzy: Baron K.
• Języki publikacji: EN

Abstrakty

EN

Inspired by J.A. Baker [1] and M. Sablik [6] we show that if x is a character of a topological group, then either a power of X is continuous or \ maps nonempty open subsets of the group onto dense subsets of the circle. As a corollary we obtain established in [2] theorem of van der Corput for functionals on topological vector spaces satisfying the congruence (1).

Słowa kluczowe

EN

topological group character; Cauchy functional congruence

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 65--69
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Baron K.

• Uniwersytet Śląski, Instytut Matematyki, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] J. A. Baker, On some mathematical characters, Glasnik Mat. 25 (45) (1990), 319-328.
• [2] K. Baron and P. Volkmann, On a theorem of van der Corput, Abh. Math. Sem. Univ. Hamburg 61 (1991), 189-195.
• [3] J. G. van der Corput, Goniometrische functies gekarakteriseerd door een functionaalbetrekking, Euclides 17 (1940), 55-75.
• [4] P. Flor, Remark on Baker’s problem, Report of meeting, The twenty-eight international symposium on functional equations (August 23 - Semptember 1, 1990, Graz-Mariatrost, Austria), Aequationes Math. 41 (1991), 298.
• [5] E. Hewitt and K. A. Ross, Abstract harmonic analysis, vol. I, Die Grundlehren der Mathematischen Wissenschaften 115, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963.
• [6] M. Sablik, A functional congruence revisited, Selected topics in functional equations and iteration theory, Proceedings of the Austrian-Polish seminar (Graz, 1991), Grazer Math. Ber. 316 (1992), 181-200.

Uwagi

Dedicated to Professor J. Musielak on his 75th birthday.