INDETERMINED MOMENT PROBLEMS RELATED TO q-FUNCTIONAL EQUATIONS

摘要

For q ∈ (0, 1), p1, p2, p ∈ R_+, we characterize all the solutions of the q-functional equations (1+p2q~(1/2)x)f(qx) = q~(β-1/2)(x+p1q~(-1/2))f(x) and f(qx) = q~(β-1)(x~2+p~2q~(-1))f(x), x > 0, β ∈ R, and we also show that these solutions solve corresponding indetermined moment problems.