Please use this identifier to cite or link to this item: `http://hdl.handle.net/11455/18129`
 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 摘要: 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(P)△f(x)=g(x),x>0 f(1)= an assigned value in Xwhere 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. URI: http://hdl.handle.net/11455/18129 Appears in Collections: 應用數學系所

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