Research On Finite Operator-Valued Frames And Modular Frames | Posted on:2013-07-29 | Degree:Master | Type:Thesis | Country:China | Candidate:J Jia | Full Text:PDF | GTID:2230330362471120 | Subject:Basic mathematics | Abstract/Summary: | PDF Full Text Request | In this paper, we study finite operator-valued frames on Hilbert spaces and finite modular framesin finite generated Hilbert C*modules.The main results obtained in this paper are listed as follows:(1) We show that every operator-valued frame on a Hilbert space either can be written as notonly, a sum of three orthonormal operator valued frames but also, a linear combination of anorthonormal operator valued frame and a Riesz operator valued frame;(2) Let {V j}j{Vj}j∈J Jbe a operator-valued frame on a Hilbert space H, and R be a subset of J. Anecessary and sufficient condition determined by the subset R such that {V j}j{Vj}j∈J Rcis still anoperator-valued frame for H is given;(3) We study the similarity and duality for finite operator-valued frame. Also, it is shown that theequal-norm Parseval operator-valued frames are optimal in the case that one packet of data is lost insignal transmission;(4) We study frames potential of modular frames for finite generated Hilbert C*modules. | Keywords/Search Tags: | finite operator-valued frame, frame operator, analysis operator, optital frames, finitemodular frames, frames potential | PDF Full Text Request | Related items |
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