컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0552 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Analysis (real / complex / harmonic analysis) (SS-08) |
| 영문제목 (Title(Eng.)) |
[CANCELLED] Inclusion relations among Euler, Taylor and Abel-type methods of summability in non-Archimedean fields |
| 저자(Author(s)) |
V. Srinivasan1, R. Deepa1 SRM University, Chennai, India1 |
| 초록본문(Abstract) | In this paper, we introduce Abel-type method of summability in a complete, non-trivially valued, non-archimedean field $K$. We also introduce the products of the transformations such as Euler, Taylor and Abel-type and prove inclusion relations among them in $K$. Let $q \in K$ be such that $|q| < 1$. The Abel-type method of order $q$ or the $[S, q]$ method is given by the matrix $(s_{n,k}^{(q)})$ as follows.\\ If $q \neq 0$ \[s_{n,k}^{(q)} = \begin{cases} 0, & k > n; \\ (n+k)C_k q^k (1-q)^{n+1}, & k \leq n. \end{cases}\] Let $p \in K$ be such that $|1-p| < 1$. The Euler method $[E, p]$ is given by the matrix $(e_{n,k}^{(p)})$ as follows:\\ If $p \neq 1$, \[e_{n,k}^{(p)} = \begin{cases} nC_k p^k (1-p)^{n-k}, & k \leq n; \\ 0, & k > n. \end{cases}\] If $p = 1$, \[e_{n,k}^{(1)} = \begin{cases} 1, & k = n; \\ 0, & k \neq n. \end{cases}\] $(e_{n,k}^{(p)})$ is called the $[E, p]$ matrix.\\ We prove an inclusion theorem as follows:\\ If $|1-p| < 1$ and $|q| < 1$ then $[S, q] \supset [E, p]$. |
| 분류기호 (MSC number(s)) |
40G, 46S |
| 키워드(Keyword(s)) | complete ultrametric fields, regular summability methods, Euler method, Taylor method, Abel-type method |
| 강연 형태 (Language of Session (Talk)) |
English |