• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.823-829
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• 2014

Ruled submanifolds in Euclidean space satisfying some algebraic equations concerning the Laplace operator related to the isometric immersion and Gauss map are studied. Cylinders over a finite type curve or generalized helicoids are characterized with such algebraic equations.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.413-425
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• 2001

We use the branching rules on SU(3) to show that if two Aloff-Wallach spaces $M_{k,l}\;and\;M_{k',l'}$ are isospectral for the Laplacian acting on smooth functions, they are isometric. We also show that 1 is the non-zero smallest eigenvalue among all Aloff-Wallach spaces and compute the multiplicities.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.313-325
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• 2010

General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed, and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.43-65
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• 2015

We present a new convergence analysis of popular Broyden's method in the Banach/Hilbert space setting which is applicable to non-smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying assumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden's iterations. To demonstrate practical merits of Broyden's method, we use it for numerical solution of three nontrivial infinite-dimensional problems.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1229-1236
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• 2009

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.187-198
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• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.19-40
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• 2007

Let L be the differential operator, Lu = $u_{tt}+u_{xxxx}$. We consider nonlinear beam equations, Lu + $bu^+$ = j, in H, where H is the Hilbert space spanned by eigenfunctions of L. We reveal the existence of multiple solutions of the nonlinear beam problems by critical point theorems.

• Honam Mathematical Journal
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• v.30 no.1
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.947-952
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• 1993

A simplified pole-placement design method is developed by analysing dynamic characteristics of the switching dynamics. Unlike the design procedure of conventional pole-placement, in the proposed method, overall state-space is directly decomposed into two invariant subspaces by the projection operator which is defined in the equivalent system, and then the closed-loop poles are assigned to each subspace independently. Hence, computations for state-feedback gain matrix are easy and simple.

• East Asian mathematical journal
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• v.24 no.1
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• pp.1-6
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• 2008

In this paper, we introduce a system of nonlinear variational inclusions involving (A, $\eta$)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, $\eta$)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.