• Honam Mathematical Journal
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• v.39 no.1
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• pp.83-91
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• 2017

In this note we consider weakly hyponormal weighted shift. In particular, we focus on the weak 4-hyponormality of the weighted shift with the Bergman tail. This is related to the open question of finding a polynomially hyponormal non-subnormal weighted shift.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.217-223
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• 2012

In this note we examine the effects on subnormality of adding a new weight or changing some weights for a given subnormal weighted shift. We consider a subnormal weighted shift with a positive point mass at the origin by means of continuous functions. Finally, we introduce some methods for evaluating point mass at the origin about moment measures associated with weighted shifts.

• Honam Mathematical Journal
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• v.26 no.2
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• pp.147-153
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• 2004

We provide some sufficient conditions for the adjoint of a unilateral weighted shift operator on a Hilbert space to be cyclic.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1031-1040
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• 2014

In this paper, we show that any cubically hyponormal weighted shift with first two equal weights is flat. And we give an example of a weighted shift which is not cubically hyponormal but almost-cubically hyponormal.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.347-352
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• 2000

In this note we answer to a question of Curto: Non-first two equal weights in the weighted shift force subnormality in the presence of quadratic hyponormality. Also it is shown that every hyponormal weighted shift with two equal weights cannot be polynomially hyponormal without being flat.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.6
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• pp.1964-1981
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• 2014

An improved Mean-Shift (MS) tracker called joint CB-LBWH, which uses a combined weighted-histogram scheme of CBWH (Corrected Background-Weighted Histogram) and LBWH (likelihood-based Background-Weighted Histogram), is presented. Joint CB-LBWH is based on the notion that target representation employs both feature saliency and confidence to form a compound weighted histogram criterion. As the more prominent and confident features mean more significant for tracking the target, the tuned histogram by joint CB-LBWH can reduce the interference of background in target localization effectively. Comparative experimental results show that the proposed joint CB-LBWH scheme can significantly improve the efficiency and robustness of MS tracker when heavy occlusions and complex scenes exist.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.25-31
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• 2022

Let α = {α_n}^∞_n=0 be a weight sequence and let W_α denote the associated unilateral weighted shift on 𝑙²(Z₊). In this paper we will investigate which weighted shift is M-hyponormal.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.81-93
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• 2020

Let m ∈ ℕ₀, p > 1 and $${\alpha}^{[m,p]}(x)\;:\;{\sqrt{x}},\;\{{\sqrt{\frac{(m+n-1)p-(m+n-2)}{(m+n)p-(m+n-1)}}}\}^{\infty}_{n=1}$$. In this paper, we consider the backward extensions of Bergman-type weighted shift W_α^[m,p](x). We consider its subnormality, k-hyponormality and positive quadratic hyponormality. Our results include all the results on Bergman weighted shift W_α(x) with m ∈ ℕ and $${\alpha}(x)\;:\;{\sqrt{x}},\;{\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m}{m+2}},\;{\sqrt{\frac{m+2}{m+3}},{\cdots}$$.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.437-460
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• 2024

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 γ is said to be infinitely divisible if for any p > 0, the sequence γ^p = {γ^p_n}^∞_n=0 is positive definite. For sequences α = {α_n}^∞_n=0 of positive real numbers, we consider the weighted shift operators W_α. It is also known that W_α is moment infinitely divisible if and only if the sequences {γ_n}^∞_n=0 and {γ_n+1}^∞_n=0 of W_α are infinitely divisible. Here γ is the moment sequence associated with α. We use conditional positive definiteness to establish a new criterion for moment infinite divisibility of W_α, which only requires infinite divisibility of the sequence {γ_n}^∞_n=0. Finally, we consider some examples and properties of weighted shift operators having the property of (k, 0)-CPD; that is, the moment matrix M_γ(n, k) is CPD for any n ≥ 0.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.673-678
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• 2008

Let $W_{\alpha}$, be a recursively generated quadratically hyponormal weighted shift with a weight sequence ${\alpha}$ : 1, (1, $\sqrt{x}$, $\sqrt{y}$)$^{\wedge}$. In [4] Curto-Jung showed that R = {(x,y) : $W_{1,\;(1,\;{\sqrt{x}},\;{\sqrt{y}})^{\wedge}}$ is quadratically hyponormal} is a closed convex with nonempty interior, which guarantees that there are a lot of quadratically hyponormal weighted shifts with first two equal weights. They suggested a problem computing expressions of certain extremal points of R. In this note we obtain a partial answer of their extremal problem.