On Banach subalgebras of the Dirichlet Hardy algebra $$\mathscr {H}^\infty $$ consisting of lacunary Dirichlet series
Year: 2026
Type: article
Abstract: Let $$\mathscr {H}^\infty $$ H ∞ be the set of all Dirichlet series $$\textstyle f\!=\!{{\sum \limits _{n=1}^\infty }} a_nn^{-s}$$ f = ∑ n = 1 ∞ a n n - s (where $$a_n\!\in \mathbb {C}$$ a n ∈ C for all $$n\!\in \! \mathbb {N}\!=\!\{1,2,3,\cdots \}$$ n ∈ N = { 1 , 2 , 3 , ⋯ } ) that converge at each s in the half-plane $$\mathbb {C}_0\!:=\!\{s\!\in \! \mathbb {C}\!:\! \text {Re}(s)\!>\!0\}$$ C 0 : = { s ∈ C : Re ( s ) > 0 } , such that $$\Vert f\Vert _{\infty }\!=\!\sup _{s\in \mathbb {C}_0}\!|f(s)|\!<\!\infty $$ ‖ f ‖ ∞ = sup s ∈ C 0 | f ( s ) | < ∞ . Then $$\mathscr {H}^\infty $$ H ∞ is a Banach algebra with pointwise operations and the supremum norm $$\Vert \cdot \Vert _\infty $$ ‖ · ‖ ∞
Author: Amol Sasane
Institution: London School of Economics and Political Science
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7124864127