Haar bases for L2(ℝn) and algebraic number theory

Journal of Number Theory

Volumn 57, Issue 1, 1996, Pages 181-197

  Lagarias, Jeffrey C ^a   Wang, Yang ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030102628     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.1996.0042     Document Type: Article

References (20)

1. 1. I. O. ANGELL, A table of complex Cubic Fields, Bull. Lond. Math. Soc. 5 (1973), 37-38.
2. n, Proc. Amer. Math Soc. 112 (1991), 549-562.
3. 3. I. DAUBECHIES, "Ten Lectures on Wavelets," CBMS Volume 61, SIAM, Philadelphia, 1992.
4. 4. B. N. DELONE AND D. K. FADDEEV, "The Theory of Irrationalities of the Third Degree," Amer. Math. Soc. Providence, RI, 1964.
5. 5. J. Graf von Schmettow, KANT - a tool for computations in algebraic number fields, in "Computational Number Theory" (A. Pethö, M. E. Pohst, H. C. Williams, and H. G. Zimmer, Eds.), pp. 291-330, de Gruyter, Berlin, 1991.
6. 6. K. GRÖCHENIG AND A. HAAS, Self-Similar Lattice Tilings, J. Fourier Analysis Appl. 1 (1994), 131-170.
7. 7. K. GRÖCHENIG AND W. MADYCH, Multiresolution analysis, Haar bases, and self-similar tilings, IEEE Trans. Inform. Theory 38 (1992), 556-568.
8. 8. A. HAAR, Zur Theorie der orthogonalen Funktionen-Systeme, Math. Ann. 69 (1910), 331-371.
9. 9. R. KENYON, Self-replicating tilings, in "Symbolic Dynamics and Its Applications" (P. Walters, Ed.), Contemporary Math., Vol. 135, pp. 239-264, 1992.
10. n, Adv. Math., to appear.
11. n I. Standard and nonstandard digit sets, J. London Math. Soc., to appear.
12. n II. Lattice tilings, preprint, 1994.
13. 2, J. Fourier Analysis Appl. 2 (1995), 1-14.
14. 14. P. G. LEMARIÉ, La propriété de support minimal dans les analyses multirésolution, C.R. Acad. Sci Paris 312 (1991), 773-776.
15. 2(ℝ), Trans. Amer. Math. Soc. 315 (1989), 69-87.
16. 16. Y. MEYER, Ondelettes, fonctions splines et analyses graduées, Cahiers Math. de la Decision 8703, Ceremade, 1986.
17. 17. M. NEWMAN, "Integral Matrices," Academic Press, New York, 1972.
18. 18. A. M. ODLYZKO, Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results, Sem. Theorie Nombres, Bordeaux 2 (1991), 119-141.
19. 19. R. S. STRICHARTZ, Wavelets and self-affine tilings, Construct. Approx. 9 (1983), 327-346.
20. 20. O. TAUSSKY, On matrix classes corresponding to an ideal and its inverse, Illinois J. Math, 1 (1957), 108-113.