tailieunhanh - Doctor of Philosophy in Mathematics: Linear and Non-linear Operators, and The Distribution of Zeros of Entire Functions

An important chapter in the theory of distribution of zeros of entire functions pertains to the study of linear operators acting on entire functions. This dissertation presents new results involving not only linear, but also some non-linear operators. | LINEAR AND NON-LINEAR OPERATORS AND THE DISTRIBUTION OF ZEROS OF ENTIRE FUNCTIONS A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI I AT MANOA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS AUGUST 2013 By Rintaro Yoshida Dissertation Committee George Csordas Chairperson Thomas Craven Erik Guentner Marcelo Kobayashi Wayne Smith ACKNOWLEDGMENTS I would like to express my deepest gratitude to my advisor Dr. George Csordas for his patience enthusiasm and support throughout the years of my studies. The completion of this dissertation is mainly due to the willingness of Dr. Csordas in generously bestowing me countless hours of advice and insight. The members of the dissertation committee who willingly accepted to take time out of their busy schedules to review comment and attend the defence regarding this work deserve great recognition. I would like to thank Dr. Pavel Guerzhoy for his understanding when I decided to change my area of study. As iron sharpens iron fellow advisees Dr. Andrzej Piotrowski Dr. Matthew Chasse Dr. Lukasz Grabarek and Mr. Robert Bates have my greatest appreciation in allowing me to take part in honing my ability to understand our beloved theory of distribution of zeros of entire functions. I appreciate everyone in the Mathematics department but in particular Austin Anderson Mike Andonian John and Tabitha Brown William DeMeo Patricia Goldstein Alex Gottlieb Zach Kent Sue Hasegawa Mike Joyce Shirley Kikiloi Troy Ludwick Alicia Maedo John Marriot Chi Mingjing Paul Nguyen Geoff Patterson John Radar Gretel Sia Jacob Woolcutt Diane Yap and Robert Young for their congeniality. Financial support was received from the University of Hawai i Graduate Student Organization for travel expenses to Macau China and the American Institute of Mathematics generously provided funding for travel and accommodation expenses in hosting the workshop Stability hyperbolicity and zero location of .