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CHARACTERIZATIONS OF GABOR FRAMES
Sumi JANG,Byeongseon JEONG,Hong Oh KIM 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5
For positive integers N, M ∈ N, let gn, ∈ L²(R) with supp(Dbgn) ∪ supp(Dbgn) ⊂ [0, M], where Dbg(t) := b<SUP>?1/2</SUP>g(t/b), b > 0 and n = 1, 2, ...,N. We give another set of necessary and sufficient conditions for the multiwindow Gabor system (GN; a, b) := {gn;k,l(t) := gn(t ? ka)e<SUP>2πilbt</SUP>}n=1,...,N; k,l∈Z and the corresponding Gabor system (GN; a, b) to form a pair of dual frames for the rational sampling ab = P/Q with P,Q ∈ N, in addition to the Zibulski-Zeevi and Janssen conditions. The conditions come from the back transform of Zibulski-Zeevi condition to the primal domain but are more informative for the applications. As an applications, we show that the Gabor system (GN; 1, 1) forms an orthonormal basis for L²(R) if and only if N = 1 and |g₁(t)| = ∑M?1m=0 xm+Em(t) a.e. where {Em m=0,...,M?1 forms Lebesgue measurable partition of the unit interval [0, 1). Our criterions provides a rich family of multiwindow dual Gabor frames and multiwindow tight Gabor frames for L²(R) for the particular choices of P, Q, N, M ∈ N.
배옹호(Yong-Ho Bae),황석원(Seogwon Hwang),정장훈(Jang Hoon Chung),정현주(Hyun-Ju Jung),김지수(Jisoo KIm),서병선(Byeongseon Seo),고명주(Myoung-Ju Koh) 과학기술정책연구원 2016 정책연구 Vol.- No.-
As the R&D capability of private sector increases, it is needed to change the role of the government from driving national R&D to supporting the private R&D. To rearrange the role of the government in R&D, this study focuses on analyzing R&D investment of the government and the private sector and tries to suggest policy implications. This research questions are as follows. 1) What is the optimal resource allocation between the governmnet and the private sector? 2) What are the effects of government R&D investment on private R&D investment? Are the effects of government R&D investment on the economic growth bigger than the private R&D investment? Is the government R&D investment crowding out the private R&D investment? 3) What are the effects of government R&D policy tools on private R&D investment? To answer these questions, we use the several analysis methodology such as portfolio analysis, econometric tools, survey of corporate recognition, and so on. Wrapping up the discussions, this research raised several policy implications. Firstly, the government has to raise up the efficiency of the government R&D. Secondly, the main areas of government R&D investment need to change from development technology to basic research. And the government has to try support small-meduim size enterprises(SMES), to make more highly vaule-added industry in our country. Thirdly, it is needed to change from the government led R&D system to market led R&D system. Fourthly, it is suggested the desirable technology innovation policies of the future growth engines.