We give a characterization of lacunary series in the Bloch space of the unit ball in C in terms of Taylor coefficients. We also characterize Bloch functions whose Taylor coefficients are nonnegative. The corresponding problems for BMOA are discussed as well.

We give an asymptotic expansion for the Taylor coefficients of L(P (z)) where L(z) is analytic in the open unit disc whose Taylor coefficients vary ‘smoothly’ and P (z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

Universit .2012.07.0 Abstract A Taylor collocation method has been developed to solve the systems of high-order linear differential–difference equations in terms of the Taylor polynomials. Using the Taylor collocation points, this method transforms differential–difference equation systems and the given conditions to matrix equations with unknown Taylor coefficients. By means of the obtained mat...

In their work, Serre and Swinnerton-Dyer study the congruence properties of the Fourier coefficients of modular forms. We examine similar congruence properties, but for the coefficients of a modified Taylor expansion about a CM point τ . These coefficients can be shown to be the product of a power of a constant transcendental factor and an algebraic integer. In our work, we give conditions on τ...

Abstract For analytic functions g on the unit disk with non-negative Maclaurin coefficients, we describe boundedness and compactness of integral operator $$T_g(f)(z)=\int _0^zf(\zeta )g'(\zeta )\,d\zeta $$ T g ( f ) </mm...