We prove the existence of dense linear subspaces, of infinitely generated subalgebras and of infinite dimensional Banach spaces in the disc algebra all of whose nonzero members are not α-h¨olderian at any point of the ...

A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles in D expanding out to the unit circle such that f goes to infinity as |z| goes to 1 through these ...

Given s ∈ (1, 2], we study (among other questions) the algebraic genericity of the set of continuous functions f : [0, 1] → R whose graph has Hausdorff (or Box) dimension exactly s.

We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose non-null functions are nowhere differentiable at the boundary. Infinitely generated free ...