A Note on the Structure of Affine Subspaces of *L*^{2}(R^{d})

ABSTRACT

This paper investigates the structure of general affine subspaces of *L*^{2}(R* ^{d}*) . For a

Cite this paper

Zhou, F. and Xu, X. (2015) A Note on the Structure of Affine Subspaces of*L*^{2}(R^{d}). *Advances in Pure Mathematics*, **5**, 62-70. doi: 10.4236/apm.2015.52008.

Zhou, F. and Xu, X. (2015) A Note on the Structure of Affine Subspaces of

References

[1] Weiss, G. and Wilson, E.N. (2001) The Mathematical Theory of Wavelets. In: Byrnes, J.S., Ed., Twentieth Century Harmonic Analysis-A Celebration//Proceedings of the NATO Advanced Study Institute, Kluwer Academic Publishers, Dordrecht, 329-366.

[2] Dai, X., Diao, Y., Gu, Q. and Han, D. (2002) Frame Wavelets in Subspaces of . Proceedings of the American Mathematical Society, 130, 3259-3267. http://dx.doi.org/10.1090/S0002-9939-02-06498-5

[3] Zhou, F.Y. and Li, Y.Z. (2010) Multivariate FMRAs and FMRA Frame Wavelets for Reducing Subspaces of . Kyoto Journal of Mathematics, 50, 83-99. http://dx.doi.org/10.1215/0023608X-2009-006

[4] Dai, X., Diao, Y. and Gu, Q. (2002) Subspaces with Normalized Tight Frame Wavelets in . Proceedings of the American Mathematical Society, 130, 1661-1667. http://dx.doi.org/10.1090/S0002-9939-01-06257-8

[5] Dai, X., Diao, Y., Gu, Q. and Han, D. (2003) The Existence of Subspace Wavelet Sets. Journal of Computational and Applied Mathematics, 155, 83-90.

http://dx.doi.org/10.1016/S0377-0427(02)00893-2

[6] Lian, Q.F. and Li, Y.Z. (2007) Reducing Subspace Frame Multiresolution Analysis and Frame Wavelets. Communications on Pure and Applied Analysis, 6, 741-756. http://dx.doi.org/10.3934/cpaa.2007.6.741

[7] Li, Y.Z. and Zhou, F.Y. (2010) Affine and Quasi-Affine Dual Frames in Reducing Subspaces of . Acta Mathematica Sinica (Chinese Edition), 53, 551-562.

[8] Gu, Q. and Han, D. (2009) Wavelet Frames for (Not Necessarily Reducing) Affine Subspaces. Applied and Computational Harmonic Analysis, 27, 47-54. http://dx.doi.org/10.1016/j.acha.2008.10.006

[9] Gu, Q. and Han, D. (2011) Wavelet Frames for (Not Necessarily Reducing) Affine Subspaces II: The Structure of Affine Subspaces. Journal of Functional Analysis, 260, 1615-1636.

http://dx.doi.org/10.1016/j.jfa.2010.12.020

[10] Zhou, F.Y. and Li, Y.Z. (2013) A Note on Wavelet Frames for Affine Subspaces of . Acta Mathematica Sinica (Chinese Edition), 33A, 89-97.

[1] Weiss, G. and Wilson, E.N. (2001) The Mathematical Theory of Wavelets. In: Byrnes, J.S., Ed., Twentieth Century Harmonic Analysis-A Celebration//Proceedings of the NATO Advanced Study Institute, Kluwer Academic Publishers, Dordrecht, 329-366.

[2] Dai, X., Diao, Y., Gu, Q. and Han, D. (2002) Frame Wavelets in Subspaces of . Proceedings of the American Mathematical Society, 130, 3259-3267. http://dx.doi.org/10.1090/S0002-9939-02-06498-5

[3] Zhou, F.Y. and Li, Y.Z. (2010) Multivariate FMRAs and FMRA Frame Wavelets for Reducing Subspaces of . Kyoto Journal of Mathematics, 50, 83-99. http://dx.doi.org/10.1215/0023608X-2009-006

[4] Dai, X., Diao, Y. and Gu, Q. (2002) Subspaces with Normalized Tight Frame Wavelets in . Proceedings of the American Mathematical Society, 130, 1661-1667. http://dx.doi.org/10.1090/S0002-9939-01-06257-8

[5] Dai, X., Diao, Y., Gu, Q. and Han, D. (2003) The Existence of Subspace Wavelet Sets. Journal of Computational and Applied Mathematics, 155, 83-90.

http://dx.doi.org/10.1016/S0377-0427(02)00893-2

[6] Lian, Q.F. and Li, Y.Z. (2007) Reducing Subspace Frame Multiresolution Analysis and Frame Wavelets. Communications on Pure and Applied Analysis, 6, 741-756. http://dx.doi.org/10.3934/cpaa.2007.6.741

[7] Li, Y.Z. and Zhou, F.Y. (2010) Affine and Quasi-Affine Dual Frames in Reducing Subspaces of . Acta Mathematica Sinica (Chinese Edition), 53, 551-562.

[8] Gu, Q. and Han, D. (2009) Wavelet Frames for (Not Necessarily Reducing) Affine Subspaces. Applied and Computational Harmonic Analysis, 27, 47-54. http://dx.doi.org/10.1016/j.acha.2008.10.006

[9] Gu, Q. and Han, D. (2011) Wavelet Frames for (Not Necessarily Reducing) Affine Subspaces II: The Structure of Affine Subspaces. Journal of Functional Analysis, 260, 1615-1636.

http://dx.doi.org/10.1016/j.jfa.2010.12.020

[10] Zhou, F.Y. and Li, Y.Z. (2013) A Note on Wavelet Frames for Affine Subspaces of . Acta Mathematica Sinica (Chinese Edition), 33A, 89-97.