Sturm-Liouville Wavelets

Applied and Computational Harmonic Analysis

Volumn 5, Issue 2, 1998, Pages 216-247

  Depczynski, Uwe ^a  

^a UNIVERSITY OF HOHENHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007611021     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1997.0231     Document Type: Article

References (18)

1. G. Birkhoff and G.-C. Rota, "Ordinary Differential Equations," 2nd ed., New York, 1969.
2. C. K. Chui and H. N. Mhaskar, On trigonometric wavelets, Constr. Approx. 9 (1993), 167-190.
3. C. K. Chui and E. Quak, Wavelets on a bounded interval, in "Numerical Methods of Approximation Theory" (D. Braess and L. L. Schumaker, Eds.), Vol. 9, pp. 53-75, 1992.
4. A. Cohen, I. Daubechies, and P. Vial, Multiresolution analysis, wavelets and fast algorithms on the interval, Appl. Comput. Harmon. Anal. 1 (1993), 54-81.
5. J. B. Conway, "A Course in Functional Analysis," 2nd ed., Springer-Verlag, New York, 1990.
6. U. Depczynski, "Über die Konstruktion von waveletartigen Zerlegungen auf kompakten Intervallen mit Hilfe der Eigenlösungen regulärer Sturm-Liouville Probleme," Ph.D. thesis, University of Duisburg, Duisburg, 1995.
7. U. Depczynski and K. Jetter, Multiscale decompositions on the interval based on DCT-I transforms, in "Advanced Topics in Multivariate Approximation" (F. Fontanelle, K. Jetter, and P. J. Laurent, Eds.), pp. 57-70, World Scientific, Singapore, 1996.
8. U. Depczynski, K. Jetter, K. Molt, A. Niemöller, and J. Stöckler, Wavelet methods in chemometrics: Quantitative spectrometric multicomponent analysis, in "15th JMACS World Congress on Scientific Computation, Modelling and Applied Mathematics," (A. Sydow, Ed.), Vol. 1, pp. 87-92, Wissenschaft & Technik Verlag, Berlin, 1997.
9. B. Fischer and J. Prestin, Wavelets based on orthogonal polynomials, Math. Comp. 66 (1997), 1593-1618.
10. G. H. Golub and C. F. van Loan, "Matrix Computations," 2nd ed., Johns Hopkins Press, Baltimore, MD, 1989.
11. T. Kilgore and J. Prestin, Polynomial wavelets on the interval, Constr. Approx. 12 (1996), 95-110.
12. G. Plonka and M. Tasche, A unified approach to periodic wavelets, in "Wavelets: Theory, Algorithms, and Applications" (C. K. Chui, L. Montefusco, and L. Puccio, Eds.), pp. 137-151, Academic Press, Boston, 1994.
13. G. Plonka and M. Tasche, On the computation of periodic spline wavelets, Appl. Comput. Harmon. Anal. 2 (1995), 1-14.
14. M. Tasche, Polynomial wavelets on [-1, +1], in "Approximation Theory, Wavelets and Applications" (S. P. Singh, Ed.), pp. 497-512, Kluwer, Dordrecht, 1995.
15. K. Yosida, "Functional Analysis," Springer-Verlag, New York/Berlin 1974.
16. K. Yosida, "Lectures on Differential and Integral Equations," Interscience, New York, 1960.
17. D. Zwillinger, "Handbook of Differential Equations," 2nd ed., Academic Press, Boston, 1992.
18. A. Zygmund, "Trigonometric Series," 2nd ed., Cambridge Univ. Press, Cambridge, UK, 1959.