• East Asian mathematical journal
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• v.29 no.3
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• pp.259-268
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• 2013

There are a lot of unsolved problems or issues regarding Kronecker products, vec-operator and Commutation matrices. We derived further properties and results of Kronecker products, vec-operator and Commutation Matrices.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.205-210
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• 2001

We give a characterization of regular operators that allows us to prove that a bounded operator acting between Banach spaces is almost regular if and only if it is regular, solving an open problem in [5]. As an application, we show that some operators in the closure of the set of all regular operators are regular.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.353-360
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• 2000

The fundamental gap between the lowest two Dirich-let eigenvalues for a Schr dinger operator HR={{{{ { { d}^{2 } } over { { dx}^{2 } } }}}}+V(x) on L({{{{ LEFT | -R,R RIGHT | }}}}) is compared with the gap for a same operator Hs with a different domain {{{{ LEFT [ -S,S RIGHT ] }}}} and the difference is exponentially small when the potential has a large barrier.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.565-568
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• 2007

We solve the asymptotic Dirichlet problem for a certain $Schr\"{o}dinger$ operator on 2-dimensional Cartan-Hadamard manifolds.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1471-1481
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• 2016

We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.699-709
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• 2014

In the present paper, we investigate starlikeness conditions for q-differential operator by using the concept of quantum calculus in the unit disk.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.149-157
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• 2012

By means of fractional calculus techniques, we find explicit solutions of confluent hypergeometric equations. We use the N-fractional calculus operator $N^{\mu}$ method to derive the solutions of these equations.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.181-190
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• 2013

In this paper we study the Putinar's matricial model operator of rank 2 and provide some evidences for the validity of the conjecture in [8].

• East Asian mathematical journal
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• v.18 no.1
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• pp.21-41
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• 2002

In this paper, we determine the spectrum of the Rhaly matrix $R_a$ as an operator on the space by, when $lim_n(n+1)a_n{\neq}0$ and exists.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.73-76
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• 1998

It is proved that the partial differential operator $D_x + ix^q D^2_y$ is not locally solvable in any open set which intersects the line x = 0, when $q = - \frac{2l-1}{2k-1}$ is not an integer.