On the regularity of de Rham curves

Izvestiya Mathematics

Volumn 68, Issue 3, 2004, Pages 567-606

  Protasov, V Yu ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746491704     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2004v068n03ABEH000489     Document Type: Article

References (50)

1. G. de Rham, "Un peu de mathématiques à propos d'une courbe plane", Revue de Mathematiques Elementaires. II 1947:4, 5, 678-689.
2. G. de Rham, "Sur une courbe plane", J. Math. Pures Appl. 35 (1956), 25-42.
3. G. de Rham, "Sur les courbes limites de polygones obtenus par trisection", Enseignement Math. 5 (1959), 29-43.
4. G. M. Chaikin, "An algorithm for high speed curve generation", Computer Graphics and Image Processing 3 (1974), 346-349.
5. D. Cavaretta, W. Dahmen, and C. Micchelli, "Stationary subdivision", Memoirs Amer. Math. Soc. 93 (1991), 1-186.
6. N. Dyn, J. A. Gregory, and D. Levin, "Analysis of linear binary subdivision schemes for curve design", Constr. Approx. 7 (1991), 127-147.
7. G. Deslauriers and S. Dubuc, "Symmetric iterative interpolation processes", Constr. Approx. 5 (1989), 49-68.
8. I. Daubechies and J. Lagarias, "Two-scale difference equations. I. Global regularity of solutions", SIAM J. Math. Anal. 22 (1991), 1388-1410.
9. I. Daubechies and J. Lagarias, "Two-scale difference equations. II. Local regularity, infinite products of matrices and fractals", SIAM J. Math. Anal. 23 (1992), 1031-1079.
10. V. Protasov, "Refinement equations with nonnegative coefficients", J. Fourier Anal. Appl. 6:6 (2000), 55-77.
11. G. E. Farin, Curves and surfaces for computer-aided geometric design, Academic Press, San Diego 1997.
12. C. Brezinski and M. Redivo Zaglia, Extrapolation methods, theory and practice, North-Holland, New York 1991.
13. G. Aumann, "Subdivision of linear corner-cutting curves", J. Geom. Graph. 1:2 (1997), 91-103.
14. E. Mainar and J. M. Pena, "Error analysis of corner-cutting algorithms", Numer. Algorithms 22:1 (1999), 41-52.
15. N. Sidorov and A. Vershik, "Ergodic properties of Erdös measure, the entropy of golden shift, and related problems", Monatsh. Math. 126 (1998), 215-261.
16. P. Nikitin, "The Hausdorff dimension of the harmonic measure on the de Rham curve", Proc. Sem. St.-Petersburg Inst. Math. (POMI) 283 (2001), 206-222. (Russian)
17. M. Paluszny, H. Prautzsch, and M. Schafer, "A geometric look at corner cutting", Comput. Aided Geom. Design 14 (1997), 421-447.
18. J.-L. Merrien, "Prescribing the length of a de Rham curve", Math. Engrg. Indust. 7:2 (1998), 129-138.
19. S. Dubuc, J.-L. Merrien, and P. Sablonniere, "The length of the de Rham curve", J. Math. Anal. Appl. 223:1 (1998), 182-195.
20. J. A. Gregory and R. Qu, "Non-uniform corner cutting", Comput. Aided Geom. Design 13 (1996), 763-772.
21. L. Noakes, "Nonlinear corner cutting", Adv. Comput. Math. 8:3 (1998), 165-177.
22. J. E. Hutchinson, "Fractals and self-similarity", Indiana Univ. Math. J. 30 (1981), 713-747.
23. M. Barnsley, Fractals everywhere, Academic Press, Boston 1988.
24. G. A. Micchelli and H. Prautzsch, "Uniform refinement of curves", Linear Algebra Appl. 114/115 (1989), 841-870.
25. D. Collela and C. Heil, "Characterization of scaling functions. I. Continuous solutions", SIAM J. Matrix Anal. Appl. 15 (1994), 496-518.
26. O. Rioul, "Simple regularity criteria for subdivision schemes", SIAM J. Math. Anal. 23 (1992), 1544-1576.
27. B. Han, "Analysis and construction of optimal multivariate biorthogonal wavelets with compact support", SIAM J. Math. Anal. 31 (1999), 274-304.
28. L. Villemoes, "Wavelet analysis of refinement equations", SIAM J. Math. Anal 25 (1994), 1433-1460.
29. M. Vetterly and C. Herley, "Wavelets and filter banks. Theory and design", IEEE Trans. Signal Proc. 40 (1992), 2207-2232.
30. V. Yu. Protasov, "On the asymptotics of the partition function", Mat. Sb. 191:3 (2000), 65-98;
31. English transl., Sb. Math. 191 (2000), 381-414.
32. M. A. Berger and Y. Wang, "Bounded semi-groups of matrices", Linear Algebra Appl. 166 (1992), 21-27.
33. V. Blondel and J. M. Tsitsiklis, "Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard", IEEE Trans. Automat. Control 45 (2000), 1762-1765.
34. V. Blondel and J. M. Tsitsiklis, "The boundedness of all products of a pair of matrices is undecidable", Systems Control Lett. 41:2 (2000), 135-140.
35. V. Blondel, J. Theys, and A. A. Vladimirov, "An elementary counterexample to the finiteness conjecture", SIAM J. Matrix Anal. Appl. 24 (2003), 963-970; e-print http://www.inma.ucl.ac.be/~blondel/publications/01BTV- FC.pdf.
36. V. Yu. Protasov, "The joint spectral radius and invariant sets of linear operators", Fundam. Prikl. Mat. 2:1 (1996), 205-231. (Russian)
37. G. Gripenberg, "Computing the joint spectral radius, Linear Algebra Appl. 234 (1996), 43-60.
38. G.-C. Rota and G. Strang, "A note on the joint spectral radius", Kon. Nederl. Acad. Wet. Proc. 63 (1960), 379-381.
39. A. A. Kirillov and A. D. Gvishiani, Theorems and problems in functional analysis, 2nd ed., Nauka, Moscow 1988;
40. English transl. of 1st ed., Springer-Verlag, Berlin-Heidelberg-New York 1982.
41. V. I. Oseledets, "A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems", Trudy Moskov. Mat. Obshch. 19 (1968), 179-210;
42. English transl., Trans. Moscow Math. Soc. 19 (1968), 197-231.
43. J. Ma, Y. Chen, and Z. Liu, "The matrix algorithm of Lyapunov exponent for the experimental data obtained in dynamic analysis", Appl. Math. Mech. 20 (1999), 985-993.
44. K. Ravishankar, "Power-law scaling of the top Lyapunov exponent of a product of random matrices", J. Stat. Phys. 54:1/2 (1989), 531-537.
45. E. M. Kaganova, "The Lyapunov exponent of the product of random operators", Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1988, no. 2, 10-14;
46. English transl., Moscow Univ. Math. Bull. 43:2 (1988), 12-17.
47. p-solutions for two-scale dilation equations", SIAM J. Math. Anal. 26 (1995), 1018-1046.
48. V. Yu. Protasov, "The generalized spectral radius. The geometric approach", Izv. Ross. Akad. Nauk Ser. Mat. 61:5 (1997), 99-136;
49. English transl., Izv. Math. 61 (1997), 995-1030.
50. D. X. Zhow, "The p-norm joint spectral radius and its applications in wavelet analysis", AMS/IP Stud. Adv. Math. 25 (2002), 305-326.