caa a22 4500 605508925 CHVBK 20210128100638.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00010-014-0334-y doi (NATIONALLICENCE)springer-10.1007/s00010-014-0334-y On a variant of μ -Wilson's functional equation on a locally compact group [Elektronische Daten] [D. Zeglami, B. Fadli, S. Kabbaj] Let G be a locally compact group. Let σ be a continuous involution of G and letμ be a complex bounded and σ-invariant measure. We determine the continuous, bounded andμ-central solutions of the functional equation $$ \int\limits_{G} f(xty)d \mu (t) + \int\limits_{G} f(\sigma (y) tx) d \mu(t) = 2f(x)g(y),\, \quad x,y \in G. $$ ∫ G f ( x t y ) d μ ( t ) + ∫ G f ( σ ( y ) t x ) d μ ( t ) = 2 f ( x ) g ( y ) , x , y ∈ G . The paper of Stetkær (Aequationes Math 68(3):160-176, 2004) is the essential motivation for this result and the methods used here are closely related to and inspired by it. In addition, when μ is compactly supported, we will investigate the superstability of this functional equation, which is bounded by the unknown functions $${\varphi (x)}$$ φ ( x ) or $${\varphi (y)}$$ φ ( y ) . Springer Basel, 2015 Superstability nationallicence μ -Wilson's functional equation nationallicence μ -d'Alembert's equation nationallicence μ -spherical function nationallicence Zeglami D. Department of Mathematics, E.N.S.A.M, Moulay Ismail University, BP 15290, Al Mansour, Meknes, Morocco aut Fadli B. Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco aut Kabbaj S. Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco aut Aequationes mathematicae Springer Basel 89/5(2015-10-01), 1265-1280 0001-9054 89:5<1265 2015 89 10 https://doi.org/10.1007/s00010-014-0334-y 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/s00010-014-0334-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zeglami D. Department of Mathematics, E.N.S.A.M, Moulay Ismail University, BP 15290, Al Mansour, Meknes, Morocco aut NATIONALLICENCE 700 1- Fadli B. Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco aut NATIONALLICENCE 700 1- Kabbaj S. Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/5(2015-10-01), 1265-1280 0001-9054 89:5<1265 2015 89 10