Some Properties of a Singular Integral Equation with Non-Carleman Shift

Resumo

We study the distribution of roots of the function W(z) = 1−λl^−z cot(πz), z ∈ C, where l ∈ (0, 1) and λ ∈ C are parameters. The results are applied to the problem on the solvability and number of solutions of a singular integral equation in various function spaces.