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Solvability of Convolution Equations in Generalized Distribution Spaces of Beurling Type
Pahk, Dae Hyeon,Sohn, Byung Kuen 연세대학교 자연과학연구소 1989 學術論文集 Vol.23 No.-
Beurling형의 초함수공간 D´_w에서 주어진 대합연산자 S∈E´_w가 S* D´_w=D´_w, 즉 이들 공간에서 가해할 필요충분한 조건을 S의 Fourier 변환의 증가조건을 사용해서 구했다. We classify the convolution operators in the Beurling's generalized distributions which are subjective. We show that the necessary and sufficient condition of the solvability is expressed by a lower bound of the Fouries transform of convolutors.
Edge detection algorithm based on the stricly monotonic intensity variation of the edge signal
Pahk, Cherl-Soo 대불대학교 2003 大佛大學校大學院 硏究論文集 Vol.2 No.1
We propose a new algorithm for edge detection based on the general behavior of edge signal intensity, the strictly monotonic variation of intensity across edges. We introduce an extended directional derivatives beyond scaling in the pixel space in order to explain that the algorithm is adaptive to the various widths of edges and relevant as an optimal edge detection algorithm.
On Urysohn Closed Spaces and Urysohn Compact Spaces
Pahk, Chung Ki,Kim, Hong Oh 경북대학교 교육대학원 1974 논문집 Vol.5 No.-
本 論文에서는 §2 filter의 弱集積點과 Urysohn 被覆의 槪念을 導入해서 一般 Urysohn 閉空間과 Urysohn 閉空間의 特性을 求하고(定理 2.5, 따름 定理 2.6), §3 緊密空間과 一般 Urysohn 閉空間사이에 位置한 Urysohn 緊密空間을 定義하고, 그 性質과 例를 찾는다.(定理 3.4, 3.5, 例 3.2, 3.3)
A Note on Compactifications of Semitopological Semigroups
Pahk, Gee-Hyun 嶺南大學校附設 基礎科學硏究所 1981 基礎科學硏究 Vol.1 No.-
We introduced the concept of a free semitopological semigroups and showed the existence of a free semitopological semigroup F(X) over a completely regular topological space X. We also investigated some properties of a compactification of a semitopological semigroup: If S is normal, locally compact and left cancellative. Suppose that ?? is relatively compact for all compact subsets K and L of S. Then S has property ?? if and only if S is discrete countably compact.
HYPERBOLIC CONVOLUTION EQUATION IN THE BEURLING`S GENERALIZED DISTRIBUTION SPACE
Pahk, Dae-Hyeon,Sohn, Byung-Keun Korean Mathematical Society 1999 대한수학회논문집 Vol.14 No.2
We found the characterizations for convolution operators in the Beurling`s generalized distribution space to be hyperbolic.