Soft Frames in Soft Hilbert Spaces
Keyword(s):
In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft discrete frame is bounded, self-adjoint, invertible and with a bounded inverse. Furthermore, we prove that every element in a soft Hilbert space satisfies the frame decomposition theorem. This theoretical framework is potentially applicable in signal processing because the frame coefficients serve to model the data packets to be transmitted in communication networks.
1981 ◽
Vol 33
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pp. 1205-1231
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1987 ◽
Vol 39
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pp. 880-892
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2006 ◽
Vol 13
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pp. 239-253
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1980 ◽
Vol 85
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pp. 173-193
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2003 ◽
Vol 01
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pp. 17-41
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1982 ◽
Vol 23
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pp. 91-95
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1968 ◽
Vol 20
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pp. 1353-1361
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1990 ◽
Vol 42
(5)
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pp. 890-901
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