caa a22 4500 477094864 CHVBK 20180405111524.0 cr unu---uuuuu 170330e19960801xx s 000 0 eng 10.1007/BF03322177 doi (NATIONALLICENCE)springer-10.1007/BF03322177 Brzdȩk Janusz Department of Mathematics, Pedagogical University, Rejtana 16 A, 35-310, Rzeszów, Poland aut On functional which are orthogonally additive modulo Z [Elektronische Daten] [Janusz Brzdȩk] Let E be a real inner product space with dimension at least 2, D ⊂ E, f: E → R with f(x+y)−f(x)−f(y) ∈ Z for all orthogonal x,y ∈ E, and f(D) ⊂ (−γ,γ)+Z witn some real γ > 0. We prove that, under some additional assumptions, there are a unique linear functional A: E → R and a unique constant d ∈ R with f(x)−d∥x∥2−A(x) ∈ Z for x ∈ E. We also show some applications of this result to the determination of solutions F: E → C of the conditional equation: F(x+y) = F(x)F(y) for all orthogonal x,y ∈ E. Birkhäuser Verlag, Basel, 1996 Cauchy difference nationallicence Christensen measurability nationallicence Baire property nationallicence inner product space nationallicence Results in Mathematics Birkhäuser-Verlag 30/1-2(1996-08-01), 25-38 0378-6218 30:1-2<25 1996 30 25 https://doi.org/10.1007/BF03322177 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF03322177 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Brzdȩk Janusz Department of Mathematics, Pedagogical University, Rejtana 16 A, 35-310, Rzeszów, Poland aut NATIONALLICENCE 773 0- Results in Mathematics Birkhäuser-Verlag 30/1-2(1996-08-01), 25-38 0378-6218 30:1-2<25 1996 30 25 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer