ALI KHAN, SARDAR MOHIB (2010) Algebraic Properties of Entire Functions with Coefficients in Particular Valued Fields. PhD thesis, Govt. College University, Lahore.
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)|
|Uncontrolled Keywords:||Algebraic, Properties, Entire, Functions, Coefficients, Particular, Valued Fields, Polya, polynomials, function theory|
|Subjects:||Physical Sciences (f) > Mathematics(f5)|
|Deposited By:||Mr. Javed Memon|
|Deposited On:||15 Jun 2011 16:06|
|Last Modified:||15 Jun 2011 16:06|
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