ALI KHAN, SARDAR MOHIB (2010) *Algebraic Properties of Entire Functions with Coefficients in Particular Valued Fields.* PhD thesis, Govt. College University, Lahore.

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## Abstract

The study of entire functions is of central importance in complex function theory. We consider the ring of entire functions either on sub fields of C or on some sub fields 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 ezout property for the ring of entire functions over Cp independent of Mittag-Le er 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 Polya and Gel'fond on the entire functions which are polynomials. We 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.

Item Type: | Thesis (PhD) |
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Uncontrolled Keywords: | Algebraic, Properties, Entire, Functions, Coefficients, Particular, Valued Fields, Polya, polynomials, function theory |

Subjects: | Physical Sciences (f) > Mathematics(f5) |

ID Code: | 6273 |

Deposited By: | Mr. Javed Memon |

Deposited On: | 15 Jun 2011 16:06 |

Last Modified: | 15 Jun 2011 16:06 |

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