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Title: Algebraic Properties of Entire Functions with Coefficients in Particular Valued Fields
Authors: Khan, Sardar Mohib Ali
Keywords: Natural Sciences
General principles of mathematics
Issue Date: 2004
Abstract: The study of entire functions is of central importance in complex function theory. We consider the ring of entire functions either on subfields of C or on some subfields of Cp . By using a technique based on admissible filters we study the ideal structure of the ring of entire functions. Then we prove the B ́zout property for the ring of entire e functions over Cp independent of Mittag-Leffler theorem. An important problem in complex function theory is to find an entire function from its values on a given sequence. By means of so-called Newton entire functions we solve a series of interpolation problems. Then we obtain a general result which implies the results of P ́lya and Gel’fond on the entire functions which are polynomials. We o prove a similar result for the entire functions f such that f (D) ⊂ D, where D is a particular bounded set. As an application we replace the use of power series for the initial value problems for ODE’s with Newton series for boundary value problems.
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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