# On generalized d'Alembert functional equation.

Mohamed Akkouchi; Allal Bakali; Belaid Bouikhalene; El Houcien El Qorachi

Extracta Mathematicae (2006)

- Volume: 21, Issue: 1, page 67-82
- ISSN: 0213-8743

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topAkkouchi, Mohamed, et al. "On generalized d'Alembert functional equation.." Extracta Mathematicae 21.1 (2006): 67-82. <http://eudml.org/doc/41851>.

@article{Akkouchi2006,

abstract = {Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d'Alembert functional equationD(μ) ∫G f(xty)dμ(t) + ∫G f(xtσ(y))dμ(t) = 2f(x)f(y) x, y ∈ G;where f: G → C to be determined is a measurable and essentially bounded function.},

author = {Akkouchi, Mohamed, Bakali, Allal, Bouikhalene, Belaid, El Qorachi, El Houcien},

journal = {Extracta Mathematicae},

keywords = {Ecuaciones funcionales; Grupos de Lie; Grupo localmente compacto; Teoría de la representación; Operadores diferenciales; integral functional equation; Gelfand measure; locally compact Hausdorff group; commutative Banach algebra; Lie group},

language = {eng},

number = {1},

pages = {67-82},

title = {On generalized d'Alembert functional equation.},

url = {http://eudml.org/doc/41851},

volume = {21},

year = {2006},

}

TY - JOUR

AU - Akkouchi, Mohamed

AU - Bakali, Allal

AU - Bouikhalene, Belaid

AU - El Qorachi, El Houcien

TI - On generalized d'Alembert functional equation.

JO - Extracta Mathematicae

PY - 2006

VL - 21

IS - 1

SP - 67

EP - 82

AB - Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d'Alembert functional equationD(μ) ∫G f(xty)dμ(t) + ∫G f(xtσ(y))dμ(t) = 2f(x)f(y) x, y ∈ G;where f: G → C to be determined is a measurable and essentially bounded function.

LA - eng

KW - Ecuaciones funcionales; Grupos de Lie; Grupo localmente compacto; Teoría de la representación; Operadores diferenciales; integral functional equation; Gelfand measure; locally compact Hausdorff group; commutative Banach algebra; Lie group

UR - http://eudml.org/doc/41851

ER -

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