The generalized Van Vleck's equation on locally compact groups.

Authors

  • B. Fadli IBN Tofail University.
  • D. Zeglami Moulay Ismail University.
  • S. Kabbaj IBN Tofail University.

Keywords:

Functional equation, Van Vleck, Involutive automorphism, Character, Additive map

Abstract

We determine the continuous solutions ʄ, g :GC of each of the two functional equations

G{ʄ,(xyt) – ʄ(σ(y)xt)}dμ(t) = ʄ(x)g(y),   x, yG,

G{ʄ,(xyt) – ʄ(σ(y)xt)}dμ(t) = g(x)ʄ(y),   x, yG,

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.

Author Biographies

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.

References

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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).

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

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

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

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).

How to Cite

[1]
B. Fadli, D. Zeglami, and S. Kabbaj, “The generalized Van Vleck’s equation on locally compact groups.”, Proyecciones (Antofagasta, On line), vol. 36, no. 4, pp. 545-566, 1.

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