• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.177-189
• /
• 2003

For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on R^d$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi-stability with exponent Q. Characterization of strictly operator na-semi-stable distributions among operator m-semi-stable distributions is given. Translation of strictly operator m-semi-stable distribution is discussed.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.11a
• /
• pp.221-225
• /
• 2002

For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on $R^{d}$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi- stability with exponent Q. Translation of strictly operator m-semi-stable distribution is discussed.

• Kyungpook Mathematical Journal
• /
• v.51 no.3
• /
• pp.241-250
• /
• 2011

In this paper, we define new classes of analytic functions using a general derivative operator which is a unification of the S$\breve{a}$l$\breve{a}$gean derivative operator, the Owa-Srivastava fractional calculus operator and the Al-Oboudi operator, and discuss some coefficient inequalities for functions belong to this classes.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.659-669
• /
• 2022

In this paper we introduce the notion of universal free product for operator systems and operator spaces, and prove extension results for the operator system lifting property (OSLP) and operator system local lifting property (OSLLP) to the universal free product.

• Coupled systems mechanics
• /
• v.1 no.4
• /
• pp.325-343
• /
• 2012

We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1791-1809
• /
• 2018

Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

• Journal of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.703-721
• /
• 2019

The notion of slant H-Toeplitz operator $V_{\phi}$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is a slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.375-391
• /
• 1994

In 1968k Cameron and Storvick introduced the analytic and the sequential operator-valued function space integral [2]. Since then, the theo교 of the analytic operator-valued function space integral has been investigated by many mathematicians - Cameron, Storvick, Johnson, Skoug, Lapidus, Chang and author etc. But there are not that many papers related to the theory of the sequential operator-valued function space integral. In this paper, we establish the existence of the sequential operator-valued function space integral as an operator from $L_p$ to $L_p'(1 and investigated the integral equation related to this integral.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.871-884
• /
• 2000

Polyharmonic operator with Dirichlet boundary condition is considered in a n-dimensional cone. The regularity properties of weak solutions are studied. In particular, it is proved the Holder contionuity of solutions near the vertex of the cone for dimensions n=2m+3,2m+4, where 2m is the order of the polyharmonic operator.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1045-1061
• /
• 2018

We investigate the relationship between $C^*$-envelopes and inductive limit of operator systems. Various operator system nuclearity properties of inductive limit for a sequence of operator systems are also discussed.