Linear and non-linear operators, and the distribution of zeros of entire functions

Date
2013-08
Authors
Yoshida, Rintaro
Contributor
Advisor
Department
Instructor
Depositor
Speaker
Researcher
Consultant
Interviewer
Annotator
Journal Title
Journal ISSN
Volume Title
Publisher
[Honolulu] : [University of Hawaii at Manoa], [August 2013]
Volume
Number/Issue
Starting Page
Ending Page
Alternative Title
Abstract
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. If fkg1k =0 is a sequence of real numbers, and Q = fqk(x)g1k=0 is a sequence of polynomials, where deg qk(x)= k, associate with the sequence fkg1k =0 a linear operator T such that T[qk(x)]=kqk(x), k = 0; 1; 2; : : : . The sequence fkg1k =0 is termed a Q-multiplier sequence if T is a hyperbolicity preserving operator. Some multiplier sequences are characterized when the polynomial set Q is the set of Jacobi polynomials. In a related question, a family of second order differential operators which preserve hyperbolicity is established. It is shown that a real entire function '(x), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of '(x) to belong to the Laguerre-P olya class. Recently, P. Br and en proved a conjecture due to S. Fisk, P. R. W. McNamara, B. E. Sagan and R. P. Stanley. The result of P. Br and en is extended, and a related question posed by S. Fisk regarding the distribution of zeros of polynomials under the action of certain non-linear operators is answered.
Description
Ph.D. University of Hawaii at Manoa 2013.
Includes bibliographical references.
Keywords
Laguerre-type
Citation
Extent
Format
Geographic Location
Time Period
Related To
Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Mathematics.
Table of Contents
Rights
Rights Holder
Local Contexts
Email libraryada-l@lists.hawaii.edu if you need this content in ADA-compliant format.