A Disproof of a Conjecture of Robertson and Generalizations
For a -function on the unit ball we define the Bloch norm by where is the invariant derivative of and then show that
An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.
Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.