On Banach subalgebras of the Dirichlet Hardy algebra H^ consisting of lacunary Dirichlet series

Key Points

• The aim is to investigate Banach subalgebras of the Dirichlet Hardy algebra consisting of lacunary Dirichlet series.
• Defined the set $$\mathscr {H}^\infty$$ and its properties.
• Examined the convergence of Dirichlet series in the half-plane $$\mathbb {C}_0$$.
• Analyzed pointwise operations and the supremum norm within this algebra.
• Identified key properties of $$\mathscr {H}^\infty$$ as a Banach algebra.
• Demonstrated that series converge for selected values of $$s$$ in the half-plane.
• Explored implications for lacunary series in this context.