On Blaschke products diverging everywhere on the boundary of the unit disc

Abstract

If the moduli of the zeros of a Blaschke product increase sufficiently slowly the arguments of the zeros may be so chosen that the product diverges everywhere on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartSet z colon StartAbsoluteValue z EndAbsoluteValue equals 1 EndSet"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mi>z</mml:mi> <mml:mo>:</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>z</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:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{ z:|z| = 1\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Locations

• Proceedings of the American Mathematical Society - View - PDF