Sampling theory in abstract reproducing Kernel Hilbert space = 추상적 Reproducing Kernel 힐버트 공간에서의 샘플링 이론

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Let H be a separable Hilbert space and k(t) a H-valued function on a subset Ω of the real line $\mathbb{R}$ such that {k(t) |t ∈ Ω}$ is total in H. Then {f_x(t):={x, k(t)_H|x ∈ H} becomes a reproducing kernel Hilbert space (RKHS) in a natural way. Here, we develop a sampling formula for functions in this RKHS, which generalizes the well-known celebrated Whittaker-Shannon-Kotel``nikov (WSK) sampling formula in the Paley-Wiener space of band-limited signals. To be more precise, we develop a multi-channel sampling formula in which every channel is given arbitrary chosen sampling points.
Advisors
Kwon, Kil-Hyunresearcher권길헌researcher
Description
한국과학기술원 : 응용수학전공,
Publisher
한국과학기술원
Issue Date
2005
Identifier
243538/325007  / 020033681
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 응용수학전공, 2005.2, [ iii, 24 p. ; ]

Keywords

Reproducing Kernel Hilbert space; Sampling theory; Multi-channel samplinges; 다중채널 샘플링; Reproducing Kernel 힐버트 공간; 샘플링 이론; tree-structured approach

URI
http://hdl.handle.net/10203/42123
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=243538&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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