Wavelets associated with periodic basis functions

Applied and Computational Harmonic Analysis

Volumn 3, Issue 1, 1996, Pages 40-56

  Narcowich, Francis J ^a   Ward, Joseph D ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002546569     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1996.0003     Document Type: Article

References (17)

1. d), Trans. Amer. Math. Soc. 341 (1994), 787-806.
2. E. Breitenberger, Uncertainty measures and uncertainty relations for angle observables, Found. Phys. 15 (1983), 353-364.
3. C. K. Chui and H. N. Mhaskar, On trigonometric wavelets, Constr. Approx. 9 (1993), 167-190.
4. C. K. Chui, J. Stöckler, and J. D. Ward, Analytic wavelets generated by radial functions, Adv. Comput. Math., to appear.
5. G. B. Folland, "Fourier Analysis and Its Applications," Wadsworth & Brooks/Cole, Pacific Grove, CA, 1992.
6. Y. W. Koh, S. L. Lee, and H. H. Tan, Periodic Orthogonal Splines and Wavelets, Appl. Comput. Harmonic Anal. 2 (1995), 201-218.
7. W R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions, Approx. Theory Appl. 4 (1988), 77-79.
8. W R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions II, Math. Comp. 54 (1990), 211-230.
9. F. J. Narcowich, Generalized Hermite interpolation and positive definite kernels on a Riemannian manifold, J. Math. Anal. Appl. 190 (1995), 165-193.
10. G. Plonka and M. Tasche, "Periodic Spline Wavelets," Technical Report 93/4, FB Mathematik, Universität Rostock, Germany, 1993.
11. M. J. D. Powell, The theory of radial basis approximation in 1990, in "Wavelets, Subdivision and Radial Functions" (W. Light, Ed.), pp. 105-210, Oxford Univ. Press, London, 1990.
12. J. Prestin and E. Quak, "Trigonometric Interpolation and Wavelet Decomposition," Center for Approximation Theory Report No. 296, Texas A & M University, 1993.
13. I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96-108.
14. J. Simmers, H. Southall, and T. O'Donnell, Advances in neural beam-forming, in "Proceedings of the 1993 Antenna Applications Symposium," Electromagnetics Laboratory, University of Illinois, Urbana-Champaign, IL, 1993.
15. G. Tolstov, "Fourier Series," Dover, New York, 1976.
16. E. T. Whittaker and G. N. Watson, "A Course of Modern Analysis," 4th ed., Cambridge Univ. Press, London, 1965.
17. Y. Xu and E. W. Cheney, Strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 116 (1992), 977-981.