The generalized Van Vleck's equation on locally compact groups

  • B. Fadli IBN Tofail University.
  • D. Zeglami Moulay Ismail University.
  • S. Kabbaj IBN Tofail University.
Palabras clave: Functional equation, Van Vleck, involutive automorphism, character, additive map.

Resumen

We determine the continuous solutions ʄ, g :G → C of each of the two functional equations  where G is a locally compact group, σ is a continuous involutive automorphism on G, and μ is a compactly supported, complex-valued Borel measure on G.

Biografía del autor

B. Fadli, IBN Tofail University.
Department of Mathematics, Faculty of Sciences.
D. Zeglami, Moulay Ismail University.
Department of Mathematics, E.N.S.A.M.
S. Kabbaj, IBN Tofail University.
Department of Mathematics, Faculty of Sciences.

Citas

[1] Ebanks, B. R., Stetkær, H.: d'Alembert's other functional equation on monoids with an involution. Aequationes Math. 89(1), pp. 187-206, (2015).

[2] Fadli, B., Zeglami, D., Kabbaj, S.: A variant of Wilson's functional equation. Publ. Math. Debrecen 87(3-4), pp. 415-427, (2015).

[3] Fadli, B., Zeglami, D., Kabbaj, S.: A joint generalization of Van Vleck's and Kannappan's equations on groups. Adv. Pure Appl. Math. 6(3), pp. 179-188, (2015).

[4] Perkins, A.M., Sahoo, P.K.: On two functional equations with involution on groups related to sine and cosine functions. Aequationes Math. 89(5), pp. 1251-1263, (2015).

[5] Stetkær, H.: Functional equations on abelian groups with involution. Aequationes Math. 54(1-2), pp. 144-172, (1997).

[6] Stetkær, H.: Functional equations on groups. World Scientific Publishing Co, Singapore, (2013).

[7] Stetkær, H.: Van Vleck's functional equation for the sine. Aequationes Math. 90(1), pp. 25-34, (2016).

[8] Van Vleck, E.B.: A functional equation for the sine. Ann. Math. Second Ser. 11(4), pp. 161-165, (1910).

[9] Van Vleck, E.B.: A functional equation for the sine. Additional note. Ann. Math. 13(1/4) (1911-1912), 154, (...).

[10] Zeglami, D., Fadli, B., Kabbaj, S.: On a variant of μ-Wilson's functional equation on a locally compact group. Aequationes Math. 89(5), pp. 1265-1280, (2015).
Cómo citar
Fadli, B., Zeglami, D., & Kabbaj, S. (1). The generalized Van Vleck’s equation on locally compact groups. Proyecciones. Journal of Mathematics, 36(4), 545-566. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2534
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