Characterizations of orthonormal scale functions: A probabilistic approach

Journal of Geometric Analysis

Volumn 10, Issue 3, 2000, Pages 417-434

  Dobric V ^a   Gundy, R ^b   Hitczenko, P ^c  

^a LEHIGH UNIVERSITY   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Multiresolution analysis; Scale function; Weak convergence of probabilities

Indexed keywords

EID: 0141794021     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02921943     Document Type: Article

References (9)

1. Billingsley, P. Convergence of Probability Measures, John Wiley & Sons, New York, 1968.
2. Cohen, A. Ondelettes, analyses multirésolutions, et filtres miroir en quadrature, Ann. Inst. H. Poincaré, Anal. Nonlinéaire, 7, 439-459, (1990).
3. Daubechies, I. Ten Lectures on Wavelets, (CBMS-NSF regional conference series in applied mathematics, 61) SIAM, Philadelphia, PA, 1992.
4. Hernández, E., Wang, X., and Weiss, G. Smoothing minimally supported frequency wavelets: Part II, J. Fourier Anal. Appl., 3(1), 23-41, (1997).
5. Hernández, E. and Weiss, G. A First Course on Wavelets, CRC Press, Boca Raton, FL, 1996.
6. Mallat, S. Mulliresolution approximation and wavelets, Trans. Am. Math. Soc.. 315, 69-88, (1989).
7. Papadakis, M., Šikić, H., and Weiss, G. The characterization of low-pass filters and some basic properties of wavelets, scaling functions, and related concepts, J. Fourier Anal. Appl., 5(5), 495-521, (1999).
8. Strichartz, R. Wavelets and self-affme tilings, Constr. Approx., 9, 327-346, (1993).
9. Wojtaszczyk, P. A Mathematical Introduction to Wavelets, London Math. Soc. Student Texts 37, Cambridge University Press, Cambridge, UK, 1997.