We use the <mml:math alttext="$B$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>B</mml:mi></mml:math> and <mml:math alttext="$B^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>B</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> operators of Levin on the Classes <mml:math alttext="$P$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math> and <mml:math alttext="$P^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>P</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> and a comparison principle to prove a Gauss-Lucas Theorem for differential operators. The connection with the determination of final sets for differential operators is then clarified.

Note on a role for entire functions of the classes <mml:math alttext="$P$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math> and <mml:math alttext="$P^* $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>P</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math>

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International Journal of Mathematics and Mathematical Sciences

Note on a role for entire functions of the classes P and P*

Abstract

Copyright