Photo from archive.org
In the present paper we characterize the solutions of each of the integral functional equations $$\begin{aligned}&\int _{G}g(xyt)d\mu (t) =g(x)g(y)-f(x)f(y),\quad x,y\in G, \\&\int _{G}f(x\sigma (y)t)d\mu (t) =f(x)g(y)-f(y)g(x),\quad x,y\in G, \end{aligned}$$∫Gg(xyt)dμ(t)=g(x)g(y)-f(x)f(y),x,y∈G,∫Gf(xσ(y)t)dμ(t)=f(x)g(y)-f(y)g(x),x,y∈G,where G… Click to show full abstract
In the present paper we characterize the solutions of each of the integral functional equations $$\begin{aligned}&\int _{G}g(xyt)d\mu (t) =g(x)g(y)-f(x)f(y),\quad x,y\in G, \\&\int _{G}f(x\sigma (y)t)d\mu (t) =f(x)g(y)-f(y)g(x),\quad x,y\in G, \end{aligned}$$∫Gg(xyt)dμ(t)=g(x)g(y)-f(x)f(y),x,y∈G,∫Gf(xσ(y)t)dμ(t)=f(x)g(y)-f(y)g(x),x,y∈G,where G is a locally compact Hausdorff group, $$\sigma :G\rightarrow G$$σ:G→G is a continuous homomorphism such that $$\sigma \circ \sigma =I,$$σ∘σ=I, and $$\mu $$μ is a regular, compactly supported, complex-valued Borel measure on G.
Journal Title: Results in Mathematics
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!