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Abstract Given a complex polynomial P with zeroes z 1 , … , z d , we show that the asymptotic zero-counting measure of the iterated derivatives Q ( n… Click to show full abstract
Abstract Given a complex polynomial P with zeroes z 1 , … , z d , we show that the asymptotic zero-counting measure of the iterated derivatives Q ( n ) , n = 1 , 2 , … , where Q = R / P is any irreducible rational function, converges to an explicitly constructed probability measure supported by the Voronoi diagram associated with z 1 , … , z d . This refines Polya's Shire theorem for these functions. In addition, we prove a similar result, using currents, for Voronoi diagrams associated with generic hyperplane configurations in C m .
Keywords:
voronoi diagrams;
rational functions;
refinement rational;
functions lya;
lya method;
method construct
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
Link to full text (if available)
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recommendations!