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- W2066374976 abstract "Firstly, we study the representation of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frames in terms of linear combinations of simpler ones such as<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-orthonormal bases,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-Riesz bases, and normalized tight<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frames. Then, we study the dual and pseudodual of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frames, which are critical components in reconstructions. In particular, we characterize the dual<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frames in a constructive way; that is, the formulae for dual<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frames are given. We also give some<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frame like representations for pseudodual<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frame pairs. The operator parameterizations of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>-frames and decompositions of bounded operators are the key tools to prove our main results." @default.
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- W2066374976 date "2015-01-01" @default.
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- W2066374976 title "Decompositions ofg-Frames and Duals and Pseudoduals ofg-Frames in Hilbert Spaces" @default.
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- W2066374976 doi "https://doi.org/10.1155/2015/305961" @default.
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