• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.3
• /
• pp.327-336
• /
• 2019

In this paper, the weak laws of large numbers for sums of asymptotically almost negatively associated random vectors in Hilbert spaces are investigated. Some results in Hien and Thanh ([3]) are generalized to asymptotically almost negatively random vectors in Hilbert space.

• Honam Mathematical Journal
• /
• v.38 no.3
• /
• pp.495-506
• /
• 2016

In this paper, we introduce and investigate a new subclass of meromorphic functions associated with a certain integral operator on Hilbert space. For this class, we obtain several properties like the coefficient inequality, extreme points, radii of close-to-convexity, starlikeness and meromorphically convexity and integral transformation. Further, it is shown that this class is closed under convex linear combination.

• Korean Journal of Mathematics
• /
• v.19 no.1
• /
• pp.101-109
• /
• 2011

We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.679-688
• /
• 2014

The notion of asymptotically negative dependence for collection of random variables is generalized to a Hilbert space and the almost sure convergence for these H-valued random variables is obtained. The result is also applied to a linear process generated by H-valued asymptotically negatively dependent random variables.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.99-107
• /
• 2012

The concept of Hilbert space dissipative norm was introduced in [8] to obtain necessary and sufficient conditions for exponential stability of contraction semigroups. In the present paper we show that the same concept can also be used to derive further properties of contraction semigroups, as well as to characterize strongly stable semigroups that are not exponentially stable.

• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.125-130
• /
• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• Communications for Statistical Applications and Methods
• /
• v.21 no.4
• /
• pp.317-325
• /
• 2014

Consider a nonlinear transform ${\Phi}(x)$ of x in $\mathbb{R}^p$ to Hilbert space H and assume that the dot product between ${\Phi}(x)$ and ${\Phi}(x^{\prime})$ in H is given by < ${\Phi}(x)$, ${\Phi}(x^{\prime})$ >= K(x, x'). The aim of this paper is to propose a mathematical technique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussian kernel $K({\cdot},{\cdot})$, which is defined by $K(x,x^{\prime})={\exp}(-{\sigma}{\parallel}x-x^{\prime}{\parallel}^2)$, ${\sigma}$ > 0. Several numerical examples are given.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.3
• /
• pp.343-352
• /
• 2018

We study the complete convergence for sequences of dependent random variables in Hilbert spaces. Results are obtained for negatively associated random variables and ${\phi}$-mixing random variables in Hilbert spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.35-38
• /
• 1996

The aim of this paper is to present a characterization of Hilbert spaces in terms of the lengths of four sides and two diagonals of a parallelogram.

• Journal of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.103-108
• /
• 1995

It is a well-known classical result of Mazur and Ulam that an isometry T from a real Banach space X onto a real Banach space Y with T(0) = 0 is automatically linear[5].