• 대한수학회지
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• 제36권1호
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• pp.73-95
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• 1999

We prove that if a given complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincar inequality and the finite covering condition at infinity on each end, then every positive harmonic function on the manifold is asymptotically constant at infinity on each end. This result is a direct generalization of those of Yau and of Li and Tam.

• 대한수학회보
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• 제50권5호
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• pp.1631-1637
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• 2013

This paper generalizes the Aleksandrov problem and Mazur Ulam theorem to the case of $n$-normed spaces. For real $n$-normed spaces X and Y, we will prove that $f$ is an affine isometry when the mapping satisfies the weaker assumptions that preserves unit distance, $n$-colinear and 2-colinear on same-order.

• 호남수학학술지
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• 제30권1호
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• pp.115-118
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• 2008

A bounded linear operator T on a complex separable Hilbert space H is called a two-isometry, if $T^{*2}T^2-2T^*T+1=0$. In this paper it is shown that every two-isometry is not supercyclic. This generalizes a result due to Ansari and Bourdon.

• 충청수학회지
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• 제22권1호
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• pp.65-71
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• 2009

Let f be an 2-isometry on a non-Archimedean 2-normed space. In this paper, we prove that the barycenter of triangle is invariant for f up to the translation by f(0), in this case, needless to say, we can imply naturally the Mazur-Ulam theorem in non-Archimedean 2-normed spaces.

• 대한수학회논문집
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• 제25권4호
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• pp.609-614
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• 2010

We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schr$\ddot{o}$dinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].

• 대한수학회보
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• 제34권1호
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• pp.103-114
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• 1997

The asymptotic Dirichlet problem for harmonic functions on a noncompact complete Riemannian manifold has a long history. It is to find the harmonic function satisfying the given Dirichlet boundary condition at infinity. By now, it is well understood [A, AS, Ch, S], when M is a Cartan-Hadamard manifold with sectional curvature $-b^2 \leq K_M \leq -a^2 < 0$. (By a Cartan-Hadamard manifold, we mean a complete simply connected manifold of non-positive sectional curvature.)

• 호남수학학술지
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• 제37권3호
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• pp.281-285
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• 2015

An A-m-isometric operator is a bounded linear operator T on a Hilbert space $\mathcal{H}$ satisfying $\sum\limits_{k=0}^{m}(-1)^{m-k}T^{*^k}AT^k=0$, where A is a positive operator. We give sufficient conditions under which A-m-isometries are not N-supercyclic, for every $N{\geq}1$; that is, there is not a subspace E of dimension N such that its orbit under T is dense in $\mathcal{H}$.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2004년도 추계학술발표논문집(상)
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• pp.199-202
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• 2004

프랙탈 압축 알고리즘에서는 필요에 따라 다양한 분할 방식을 사용하고 있다. 기존에는 분할방식에 따라 다른 isometry 변환계수 값만을 사용하고 있다. 본 논문에서는 이러한 문제를 해결하기 위하여 모든 분할 방식에서 공통적으로 사용할 수 있도록 변환 가능한 isometry 변환계수 방식을 제안하였으며 이를 하드웨어로 구현하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권3호
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• pp.193-198
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• 2003

Let X and Y be n-dimensional Euclidean spaces with $n\;{\geq}\;3$. In this paper, we generalize a classical theorem of Bookman and Quarles by proving that if a mapping, from a half space of X into Y, preserves a distance $\rho$, then the restriction of f to a subset of the half space is an isometry.

• 대한수학회논문집
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• 제34권3호
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• pp.771-782
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• 2019

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.