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- W1498891873 abstract "We characterize the orthogonal frames and orthogonal multiwavelet frames in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mfenced separators=|><mml:mrow><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:math>with matrix dilations of the form<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msqrt><mml:mfenced open=| close=| separators=|><mml:mrow><mml:mtext>d</mml:mtext><mml:mtext>e</mml:mtext><mml:mtext>t</mml:mtext><mml:mi>A</mml:mi></mml:mrow></mml:mfenced></mml:msqrt><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>A</mml:mi></mml:math>is an arbitrary expanding<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>d</mml:mi><mml:mo>×</mml:mo><mml:mi>d</mml:mi></mml:math>matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function." @default.
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- W1498891873 date "2012-01-01" @default.
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- W1498891873 title "Orthogonal Multiwavelet Frames inL2Rd" @default.
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- W1498891873 doi "https://doi.org/10.1155/2012/846852" @default.
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