在這篇論文中,一個熱帶亞純函數(tropical meromorphic function)若給定有限個零根(roots)與極點(poles)還有它們的重數(multiplicities),我們證明了這個熱帶亞純函數的存在與唯一性。另外,一個熱帶週期函數(tropical periodic function)若給定一個週期區間內的有限個零根與極點還有它們的重數,我們也找到了這個熱帶週期函數的一個簡單表達式。接著,給定一個一階線性差分方程(first-order linear difference equation),我們討論了各種情況下的所有熱帶亞純函數解的表達式。最後,對於連續函數我們提供了一個它的熱帶近似函數,希望對於解差分方程的熱帶亞純函數解時能有所助益。 / In this thesis, we find the formula of tropical meromorphic function by giving finite number of roots and poles (with multiplicities). We also find a simple formula for tropical periodic function by giving finite number of roots and poles (with multiplicities) during a period [0,T). We then discuss all cases of the tropical meromorphic solution functions of first-order linear difference equation. At last, we provide a tropical approximated function of a given continuous function. We hope it is helpful in solving the tropical meromorphic solution functions of a given difference equation.
Identifer | oai:union.ndltd.org:CHENGCHI/G0097751005 |
Creators | 陳亮, Chen, Liang |
Publisher | 國立政治大學 |
Source Sets | National Chengchi University Libraries |
Language | 英文 |
Detected Language | English |
Type | text |
Rights | Copyright © nccu library on behalf of the copyright holders |
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