@article{Fadli_Zeglami_Kabbaj_1, title={The generalized Van Vleck’s equation on locally compact groups.}, volume={36}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/2534}, abstractNote={<p>We determine the continuous solutions <em>ʄ</em>, <em>g </em>:<em>G</em> → <strong>C</strong> of each of the two functional equations</p> <p>∫<sub>G</sub>{<em>ʄ</em>,(<em>xyt</em>) – <em>ʄ</em>(σ(<em>y</em>)<em>xt</em>)}<em>d</em>μ(<em>t</em>) = <em>ʄ</em>(<em>x</em>)<em>g</em>(<em>y</em>),&nbsp;&nbsp; <em>x, y</em> ∈ <em>G</em>,</p> <p>∫<sub>G</sub>{<em>ʄ</em>,(<em>xyt</em>) – <em>ʄ</em>(σ(<em>y</em>)<em>xt</em>)}<em>d</em>μ(<em>t</em>) = <em>g</em>(<em>x</em>)<em>ʄ</em>(<em>y</em>),&nbsp;&nbsp; <em>x, y</em> ∈ <em>G</em>,</p> <p>where <em>G</em> is a locally compact group, σ is a continuous involutive automorphism on <em>G</em>, and μ is a compactly supported, complex-valued Borel measure on <em>G</em>.</p>}, number={4}, journal={Proyecciones (Antofagasta, On line)}, author={Fadli, B. and Zeglami, D. and Kabbaj, S.}, year={1}, month={1}, pages={545-566} }