caa a22 4500 605509034 CHVBK 20210128100639.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00010-015-0351-5 doi (NATIONALLICENCE)springer-10.1007/s00010-015-0351-5 Jarczyk Witold Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516, Zielona Gora, Poland aut Improving regularity of solutions of a difference equation [Elektronische Daten] [Witold Jarczyk] Using some results on convex and almost convex functions defined on a locally compact Abelian group, we prove a theorem showing a "measurability implies continuity” effect for non-negative solutions of the difference equation $${\varphi(x) = \sum_{i=1}^{k}p_{i}\varphi\left(x+a_{i} \right)}$$ φ ( x ) = ∑ i = 1 k p i φ x + a i , where $${p_{1}, \ldots, p_{k} \in (0, \infty)}$$ p 1 , ... , p k ∈ ( 0 , ∞ ) and non-zero elements $${a_{1}, \ldots, a_{k}}$$ a 1 , ... , a k of the group are given. The Author(s), 2015 Haar measure nationallicence Linear difference equation nationallicence Measurable and continuous solutions nationallicence Convex and almost convex functions on groups nationallicence Aequationes mathematicae Springer Basel 89/2(2015-04-01), 383-391 0001-9054 89:2<383 2015 89 10 https://doi.org/10.1007/s00010-015-0351-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-015-0351-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jarczyk Witold Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516, Zielona Gora, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/2(2015-04-01), 383-391 0001-9054 89:2<383 2015 89 10