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• W1981978130 abstract "Let <italic>B</italic> be a Blaschke product with zeros <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace a Subscript n Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{ {a_n}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The series <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma-summation left-parenthesis 1 minus StartAbsoluteValue a Subscript n Baseline EndAbsoluteValue squared right-parenthesis slash StartAbsoluteValue 1 minus zeta overbar a Subscript n Baseline EndAbsoluteValue Superscript gamma> <mml:semantics> <mml:mrow> <mml:mo>∑<!-- ∑ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−<!-- − --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−<!-- − --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>ζ<!-- ζ --></mml:mi> <mml:mo stretchy=false>¯<!-- ¯ --></mml:mo> </mml:mover> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>γ<!-- γ --></mml:mi> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>sum {(1 - |{a_n}{|^2})} /|1 - bar zeta {a_n}{|^gamma }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=gamma greater-than-over-equals 1> <mml:semantics> <mml:mrow> <mml:mi>γ<!-- γ --></mml:mi> <mml:mo>≧<!-- ≧ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>gamma geqq 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartAbsoluteValue zeta EndAbsoluteValue equals 1> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>ζ<!-- ζ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>|zeta | = 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, has been used by P. R. Ahern, D. N. Clark, G. T. Cargo, and others in the study of the boundary behavior of <italic>B</italic> and various associated functions. In this paper the convergence of this series is shown to be equivalent to a condition on a reproducing kernel for a subspace of the Hardy space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H squared> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{H^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Some related conditions and corollaries are also given." @default.
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• W1981978130 date "1972-01-01" @default.
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• W1981978130 title "On the accumulation of the zeros of a Blaschke product at a boundary point" @default.
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