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The Integral Cosine Addition and Sine Subtraction Laws

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Abstract

In the present paper we characterize the solutions of each of the integral functional equations

$$\begin{aligned}&\int _{G}g(xyt)d\mu (t) =g(x)g(y)-f(x)f(y),\quad x,y\in G, \\&\int _{G}f(x\sigma (y)t)d\mu (t) =f(x)g(y)-f(y)g(x),\quad x,y\in G, \end{aligned}$$

where G is a locally compact Hausdorff group, \(\sigma :G\rightarrow G\) is a continuous homomorphism such that \(\sigma \circ \sigma =I,\) and \(\mu \) is a regular, compactly supported, complex-valued Borel measure on G.

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Authors and Affiliations

  1. Department of Mathematics, E.N.S.A.M, Moulay ISMAIL University, B.P. 15290 , Al Mansour, Meknes, Morocco

    Driss Zeglami

  2. Department of Mathematics, Faculty of Sciences, IBN Tofail University, B.P. 14000 , Kenitra, Morocco

    Samir Kabbaj & Mohamed Tial

Authors
  1. Samir Kabbaj
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  2. Mohamed Tial
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  3. Driss Zeglami
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Correspondence to Driss Zeglami.

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Kabbaj, S., Tial, M. & Zeglami, D. The Integral Cosine Addition and Sine Subtraction Laws. Results Math 73, 97 (2018). https://doi.org/10.1007/s00025-018-0858-x

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