On absolutely convergent exponential sums

Graphs that are not complete pluripolar

“…It may even yield 0 on D 1 ; cf. [1]. We will see that a suitable choice of a n and c n prevents this from happening.…”

“…Let A = {a n } ∞ n=1 be a countable dense subset of ∂D 1 . Under the assumptions of Theorem 1.1, there exists an a ∈ (∂D 1 ) ∩ D 2 such that a ∈ A \ {a}.…”

Notes on invariant subspaces

“…Our proof of this theorem will be closer to the approach of Brown, Shields and Zeiler [6] than to Wermer's original proof. We need a few preliminary facts.…”

Expanding the joint spectrum of pairs of commuting contractions

“…As usual, we say that a subset ∆ in D is dominating for an arc E in T if almost every point of E is a nontangential limit of a sequence of points from ∆. It is known that ∆ in D is dominating for T if and only if u ∞ = sup z∈∆ |u(z)|, for all u ∈ H ∞ (D) [7]. Similarly, we say that ∆ in D 2 is dominating for T 2 if and only if u ∞ = sup z∈∆ |u(z)|, for all u ∈ H ∞ (D 2 ).…”