On a generalization of the Selberg trace formula
We give a Hölder type estimate for normalized ρ-quasisymmetric functions, improving some results of J. Zając.
We prove a theorem on the growth of a solution of a kth-order linear differential equation. From this we obtain some uniqueness theorems. Our results improve several known results. Some examples show that the results are best possible.
Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue's integrable complex-valued function f on T, Pγ[f] is a complex-valued harmonic function in D and it coincides with the classical Poisson integral of f provided γ is the identity mapping on T. Our considerations are motivated by the...