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標題: 在巴氏空間上Δf(x)=g(x),x>0,方程式解的一些結果及其應用
Some results of solutions of the equation []f(x)=g(x),x>0, on a banach space and its pplications
作者: 謝佳男
Hsieh, Jia-Nan
關鍵字: Stirling''s formula;Banach space;△f(x)=g(x)
出版社: 應用數學系
本篇論文主要是探討在Banach空間X上對一函數g:(0,∞)→X,方程式△f(x)=g(x),x>0,的相關問題的解,其中△f(x):=f(x+1)-f(x),x>0。一般而言,此方程式若有解則其解不必然是唯一的,但若再加上一些條件限制,則可保證此解f是唯一的。最後並給予Stirling's formula 一個新的證明方法。

Let X be a real (or complex) Banach space. For a fixed function g:(0,∞)→X, we consider the following equation
f(1)= an assigned value in X
where f:(0,∞)→X and △f(x): =f(x+1)-f(x). In general, if the equation (P) has a solution ,it is not unique. For, if f is a salutation of (P) and h:R→X a periodic function with period 1, and h(1) = 0 then f + h is still a solution of the equation (P) . Theaefore it is necessary to study under what conditions the solution of the equation (P) is unique. This is one of our main objects in this paper.
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