臺灣博碩士論文加值系統

假設A是一個無窮矩陣,利用矩陣乘法A將一數列(u)轉換成另一數列(v).本篇論文的目的就是探討什麼樣的矩陣A會將動差數列轉換成動差數列,我們發現這種矩陣會跟某一類在C[0,1]上的有界線性算子有關.我們的結果不僅推廣了[1,proposition 6.6],也給出Bennett所提出的Problem 6.7[1]的部分解.

CONTENTS
1.Introduction................................................ 1
2.Preliminaries............................................... 4
3.Main Result................................................. 6
4.Matrix Version of Main Result...............................12
5.Examples....................................................16
References..................................................23

[1] G. Bennett, Inequalitiescomplimentary to Hardy, Quart.Jour.
Math. (Oxford) 49 (1998),395-432
[2] D.V. Widder, The Laplace Transform, Princeton University
Press, 1946
[3] I. Gohberg, Basic Operator Theory, Boston, Basel,
Stuttgart, 1980
[4] W. Rudin, Principle of Mathematical Analysis, MCGrae-Hill.
Inc, 1976
[5] G.H.Hardy, Divergent Series, Oxford University Press,
Oxford,1949