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• W4313486574 abstract "We study composition operators on the Hardy space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper H squared> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>mathcal {H}^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of Dirichlet series with square summable coefficients. Our main result is a necessary condition, in terms of a Nevanlinna-type counting function, for a certain class of composition operators to be compact on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper H squared> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>mathcal {H}^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. To do that we extend our notions to a Hardy space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper H Subscript normal upper Lamda Superscript 2> <mml:semantics> <mml:msubsup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>H</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>Λ<!-- Λ --></mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:annotation encoding=application/x-tex>mathcal {H}_{Lambda }^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of generalized Dirichlet series, induced in a natural way by a sequence of Beurling’s primes." @default.
• W4313486574 created "2023-01-06" @default.
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• W4313486574 date "2023-06-30" @default.
• W4313486574 modified "2023-09-27" @default.
• W4313486574 title "Composition operators and generalized primes" @default.
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• W4313486574 doi "https://doi.org/10.1090/proc/16395" @default.
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