On a variant of μ -Wilson's functional equation on a locally compact group
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| 008 | 210128e20151001xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0334-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0334-y | ||
| 245 | 0 | 0 | |a On a variant of μ -Wilson's functional equation on a locally compact group |h [Elektronische Daten] |c [D. Zeglami, B. Fadli, S. Kabbaj] |
| 520 | 3 | |a 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 ) . | |
| 540 | |a Springer Basel, 2015 | ||
| 690 | 7 | |a Superstability |2 nationallicence | |
| 690 | 7 | |a μ -Wilson's functional equation |2 nationallicence | |
| 690 | 7 | |a μ -d'Alembert's equation |2 nationallicence | |
| 690 | 7 | |a μ -spherical function |2 nationallicence | |
| 700 | 1 | |a Zeglami |D D. |u Department of Mathematics, E.N.S.A.M, Moulay Ismail University, BP 15290, Al Mansour, Meknes, Morocco |4 aut | |
| 700 | 1 | |a Fadli |D B. |u Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco |4 aut | |
| 700 | 1 | |a Kabbaj |D S. |u Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/5(2015-10-01), 1265-1280 |x 0001-9054 |q 89:5<1265 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0334-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0334-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zeglami |D D. |u Department of Mathematics, E.N.S.A.M, Moulay Ismail University, BP 15290, Al Mansour, Meknes, Morocco |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Fadli |D B. |u Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Kabbaj |D S. |u Department of Mathematics, Faculty of Sciences, IBN Tofail University, BP 14000, Kenitra, Morocco |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/5(2015-10-01), 1265-1280 |x 0001-9054 |q 89:5<1265 |1 2015 |2 89 |o 10 | ||