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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.4
- 수록면
- 437 - 460 (24page)
- DOI
- 10.4134/CKMS.c230238
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In this paper we present the weighted shift operators having the property of moment infinite divisibility. We first review the monotone theory and conditional positive definiteness. Next, we study the infinite divisibility of sequences. A sequence of real numbers $\gamma$ is said to be infinitely divisible if for any $p>0$, the sequence $\gamma^p = \{ \gamma_n^p \}_{n=0}^{\infty}$ is positive definite. For sequences $\alpha = \{\alpha_n\}^{\infty}_{n=0}$ of positive real numbers, we consider the weighted shift operators $W_{\alpha}$. It is also known that $W_{\alpha}$ is moment infinitely divisible if and only if the sequences $\{\gamma_n\}_{n=0}^{\infty}$ and $\{\gamma_{n+1}\}_{n=0}^{\infty}$ of $W_{\alpha}$ are infinitely divisible. Here $\gamma$ is the moment sequence associated with $\alpha$. We use conditional positive definiteness to establish a new criterion for moment infinite divisibility of $W_{\alpha}$, which only requires infinite divisibility of the sequence $\{\gamma_n\}_{n=0}^{\infty}$. Finally, we consider some examples and properties of weighted shift operators having the property of $(k,0)$-CPD; that is, the moment matrix $M_{\gamma}(n,k)$ is CPD for any $n \ge 0$.
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