• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1231-1249
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• 2005

By employing Chebotarev and Fagnola's sufficient conditions for conservativity of minimal quantum dynamical semigroups [7, 8], we construct the conservative minimal quantum dynamical semigroups generated by noncommutative elliptic operators in the sense of [2]. We apply our results to concrete examples.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.111-119
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• 2022

In this article, we prove that diskcyclic C₀-semigroups exist on any infinite-dimensional Banach space. We show that a C₀-semigroup (T_t)_t≥0 satisfies the diskcyclicity criterion if and only if any of T_t's satisfies the diskcyclicity criterion for operators. Moreover, we show that there are diskcyclic C₀-semigroups that do not satisfy the diskcyclicity criterion. Also, we state various criteria for diskcyclicity of C₀-semigroups based on dense sets and d-dense orbits.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.171-179
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• 1998

In this paper, we establish Trotted-Kato type convergence theoren for nonlinear semigroups generated by coaccretive operators in a hyperbolic space.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.227-274
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• 2001

In this paper we intended to discuss the following topics: (1) Notation, generalities, Markov processes. The close relationship between (generators of) Markov processes and the martingale problem is exhibited. A link between the Korovkin property and generators of Feller semigroups is established. (2) Feynman-Kac semigroups: 0-order regular perturbations, pinned Markov measures. A basic representation via distributions of Markov processes is depicted. (3) Dirichlet semigroups: 0-order singular perturbations, harmonic functions, multiplicative functionals. Here a representation theorem of solutions to the heat equation is depicted in terms of the distributions of the underlying Markov process and a suitable stopping time. (4) Sets of finite capacity, wave operators, and related results. In this section a number of results are presented concerning the completeness of scattering systems (and its spectral consequences). (5) Some (abstract) problems related to Neumann semigroups: 1st order perturbations. In this section some rather abstract problems are presented, which lie on the borderline between first order perturbations together with their boundary limits (Neumann type boundary conditions and) and reflected Markov processes.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.931-951
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• 2002

We extend the construction of Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebra given in [13] to the case of unbounded operators satiated with the von Neumann algebra. We then apply our result to give Dirichlet forms associated to the momentum and position operators on quantum mechanical systems.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.559-565
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• 2005

In this paper, we establish the convergence of semigroups that are strongly continuous on (0, $\infty$). By using Laplace transform theory, we show some properties of semigroups and the convergence result.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.23-35
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• 2012

Given a set ${\Omega}$ and the notion of bipolar valued fuzzy sets, the concept of a bipolar ${\Omega}$-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar ${\Omega}$-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar ${\Omega}$-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar ${\Omega}$-fuzzy sub-semigroup is provided, and normal bipolar ${\Omega}$-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar ${\Omega}$-fuzzy sub-semigroups become bipolar ${\Omega}$-fuzzy sub-semigroups are considered.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.125-133
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• 1996

We show that if X is a reflexive Banach space with a uniformly G$\hat{a}$teaux differentiable norm, then the convergence of semigroups acting on Banach spaces $X_n$ implies the convergence of resolvents of generators of semigroups.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.

• Journal of the Korean Mathematical Society
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• v.9 no.2
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• pp.91-99
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• 1972