• 호남수학학술지
• /
• 제32권4호
• /
• pp.633-642
• /
• 2010

In this note, we introduce the definition of the generalized analogue of Wiener measure on the space C[a, b] of all real-valued continuous functions on the closed interval [a, b], give several examples of it and investigate some important properties of it - the Fernique theorem and the existence theorem of scale-invariant measurable subsets on C[a, b].

• Journal of applied mathematics & informatics
• /
• 제23권1_2호
• /
• pp.489-496
• /
• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• 충청수학회지
• /
• 제4권1호
• /
• pp.61-69
• /
• 1991

By $C^{(1)}$[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by $${\parallel}f{\parallel}=\sup_{x{\in}[0,1]}({\mid}f(x){\mid}+{\mid}f^{\prime}(x){\mid})\text{ for }f{\in}C^{(1)}$$. By A we denote the sub algebra of $C^{(1)}$ defined by $$A=\{f{\in}C^{(1)}:f(0)=f(1)\text{ and }f^{\prime}(0)=f^{\prime}(1)\}$$. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1] onto itself.

• 대한수학회보
• /
• 제39권2호
• /
• pp.309-315
• /
• 2002

Let I be an open interval and X a complex Banach space. Let$\varepsilon\geq0\;and\;\lambda$ a non-zero complex number with Re $\lambda\neq0$. If $\varphi$ is a strongly differentiable map from I to X with $\parallel\varphi^'(t)-\lambda\varphi(t)\parallel\leq\varepsilon\;for\;all\;t\in\;I$, then we show that the distance between $\varphi$ and the set of all solutions to the differential equation y'=$\lambda$y is at most $\varepsilon/$\mid$Re\lambda$\mid$$.

• 대한수학회지
• /
• 제53권3호
• /
• pp.709-723
• /
• 2016

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}{\mathbb{R}}^n$ by $Zn(x)=(\int_{0}^{t_1}h(s)dx(s),{\cdots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $t_n$ < t is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function $Z_n$ and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function $F(x)=f(\int_{0}^{t}e(s)dx(s))$ for $x{\in}C[0,t]$, where $f{\in}L_p(\mathbb{R})(1{\leq}p{\leq}{\infty})$ and e is a unit element in $L_2[0,t]$. Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of $L_2[0,t]$ used in the transformation is independent of e and the conditioning function $Z_n$ does not contain the present positions of the generalized Wiener paths.

• 응용통계연구
• /
• 제28권6호
• /
• pp.1147-1161
• /
• 2015

오늘날 데이터는 p-차원의 공간에서 점들로써 표현되는 전통적인 형태를 벗어나 시그널(signal), 함수, 이미지(image), 모양(shape) 등과 같은 다양한 형태의 자료들이 데이터로써 고려되고 분석되고있다. 그러한 종류의 새로운 종류의 데이터 중 하나로 심볼릭 데이터(symbolic data)를 고려할 수 있다. 심볼릭 데이터는 구간(interval), 히스토그램(histogram), 목록(list), 통계표, 분포, 또는 모형 등과 같은 다양한 형태들을 가질 수 있다. 지금까지의 연구가 주로 심볼릭 데이터의 각각의 형태별 자료를 고려했다면, 본 연구에서는 이를 확장하여 수집된 히스토그램과 멀티모달의 혼합된 형태로 이루어진 자료에 대한 계층 분할적 군집분석방법을 소개하고 이를 업종별 산업재해자료의 분석을 위해 이용한다.