頁籤選單縮合
題 名 | Growth Orders of Cesàro and Abel Means of Functions in Banach Spaces |
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作 者 | 陳正忠; 蕭勝彥; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 14:3B 2010.06[民99.06] |
頁 次 | 頁1201-1248 |
分類號 | 314.751 |
關鍵詞 | Cesàro mean; Abel mean; Exponential growth order; Polynomial growth order; Co-semigroup; Cosine operator function; |
語 文 | 英文(English) |
英文摘要 | For continuous vector-valuedfunctions, we discuss relationsamong exponential and polynomial growth orders of the γ-Ces` aro mean (γ ≥ 0) and of the Abel mean. In general, the Abel mean has growth order not larger than those of Ces`aro mean has a smaller aro means, and a higher-order Ces` growth order than a lower-order Ces` aro mean. But, for a positive function in a Banach lattice, the Abel mean and all γ-Ces` aro means with γ ≥ 1 (but not with 0 ≤ γ< 1) have the same polynomial growth order. The possibility of non-equal growth orders for these means is illustrated by some examples of C0-semigroups and cosine operator functions. |
本系統中英文摘要資訊取自各篇刊載內容。