<abstract xmlns="http://www.w3.org/1999/xhtml">We develop two-channel sampling theory in the wavelet subspace <italic>V</italic>1 from the multi resolution analysis {<italic>Vj</italic>}<italic>j</italic>∈𝕫. Extending earlier results by G. G. Walter [<xref ref-type="bibr" rid="j_auom-2015-0009_ref_001_w2aab2b8c43b1b7b1ab1ab1Aa">11</xref>], W. Chen and S. Itoh [<xref ref-type="bibr" rid="j_auom-2015-0009_ref_002_w2aab2b8c43b1b7b1ab1ab2Aa">2</xref>] and Y. M. Hong et al [<xref ref-type="bibr" rid="j_auom-2015-0009_ref_005_w2aab2b8c43b1b7b1ab1ab5Aa">5</xref>] on the sampling theory in the wavelet or shift invariant spaces, we find a necessary and sufficient condition for two-channel sampling expansion formula to hold in <italic>V</italic>1.</abstract>

We develop two-channel sampling theory in the wavelet subspace V1 from the multi resolution analysis {Vj}j∈𝕫. Extending earlier results by G. G. Walter [11], W. Chen and S. Itoh [2] and Y. M. Hong et al [5] on the sampling theory in the wavelet or shift invariant spaces, we find a necessary and sufficient condition for two-channel sampling expansion formula to hold in V1.

Two-channel sampling in wavelet subspaces

Faculty of Mathematics and Computer Sciences, Korea Science Academy of KAIST,

Faculty of Mathematical Sciences, Korea Advanced Institute of Science and Technology,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Two-channel sampling in wavelet subspaces"}

We develop two-channel sampling theory in the wavelet subspace V1 from the multi resolution analysis {Vj}j∈𝕫. Extending earlier results by G. G. Walter [11],...

Two-channel sampling in wavelet subspaces

Published Online: Apr 04, 2017

Page range: 115 - 126

Received: Apr 26, 2014

Accepted: Jun 27, 2014

DOI: https://doi.org/10.1515/auom-2015-0009

Keywords
two-channel sampling, wavelet subspaces, Riesz basis

© 2015 J.M. Kim et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Two-channel sampling in wavelet subspaces

Published Online: Apr 04, 2017

Page range: 115 - 126

Received: Apr 26, 2014

Accepted: Jun 27, 2014

DOI: https://doi.org/10.1515/auom-2015-0009

Keywordstwo-channel sampling, wavelet subspaces, Riesz basis

© 2015 J.M. Kim et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
two-channel sampling, wavelet subspaces, Riesz basis