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A note on the linear independence of characteristic functions of self-similar sets

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References

  1. A. Cohen, Ondelettes, analyses multirésolution et filtres miroirs en quadrature, Ann. Inst. Poincaré7, 439–459 (1990).

    Google Scholar 

  2. S. Dahlke, W. Dahmen andV. Latour, Smooth refinable functions and wavelets obtained by convolution products. Appl. Comput. Harmon. Anal.2, 68–84 (1995).

    Google Scholar 

  3. S.Dahlke, V.Latour and M.Neeb, Generalized cardinal B-splines: stability conditions and appropriate scaling matrices. Submitted to Constr. Approx.

  4. W. Dahmen andC. A. Micchelli, Translates of multivariate splines. Linear Algebra Appl.52/53, 217–234 (1983).

    Google Scholar 

  5. I. Daubechies, Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math.41, 909–996 (1988).

    Google Scholar 

  6. K. Gröchenig, Orthogonality criteria for compactly supported scaling functions. Appl. Comput. Harmon. Anal.1, 242–245 (1994).

    Google Scholar 

  7. K.Gröchenig and A.Haas, Self-similar lattice tilings. J. Fourier Anal. Appl., to appear.

  8. K. Gröchenig andW. R. Madych, Multirésolution analysis, Haar bases, and self-similar tilings of ℝn. IEEE Trans. Inform. Th.38 (2), 556–568 (1992).

    Google Scholar 

  9. R. Q. Jia andC. A. Micchelli, Using the refinement equation for the construction of Prewavelets II: Powers of two. in “Curves and Surfaces” (P. J. Laurent, A Le Méhauté and L. L. Schumaker, Eds.), pp. 209–246, Academic Press, New York 1991.

    Google Scholar 

  10. J. C.Lagarias and Y.Wang, Self-affine tiles in ℝn. Adv. Math., to appear.

  11. J. C.Lagarias and Y.Wang, Integral self-affine tiles in ℝnI. Standard and nonstandard digit sets. To appear.

  12. A. Ron, A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution. Constr. Approx.5, 297–308 (1989).

    Google Scholar 

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Dahlke, S., Latour, V. A note on the linear independence of characteristic functions of self-similar sets. Arch. Math 66, 80–88 (1996). https://doi.org/10.1007/BF01323986

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