Bi, Ning; Dai, Xinrong; Sun, Qiyu Construction of compactly supported \(M\)-band wavelets. (English) Zbl 0926.42021 Appl. Comput. Harmon. Anal. 6, No. 2, 113-131 (1999). The asymptotic regularity of Daubechies scaling functions is studied. Examples of \(M\)-band scaling functions which are both orthonormal and cardinal are constructed for \(M\geq 3\). Reviewer: B.Rubin (Jerusalem) Cited in 1 ReviewCited in 19 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:multiresolution; \(M\)-band wavelets; cardinal function; orthonormality; regularity; Daubechies scaling functions × Cite Format Result Cite Review PDF References: [1] Ausher, P.: Ondelette et espaces de Hardy. (1989) [2] N. Bi, X. Dai, Q. Sun, Construction of Compactly SupportedM, Center for Mathematical Sciences, Zhejiang University, 1995 [3] De Boor, C.; Devore, R. A.; Ron, A.: On the constructions of multivariate (pre)wavelets. Constr. approx. 9, 123-166 (1993) · Zbl 0773.41013 [4] Chui, C. K.: An introduction to wavelets. (1992) · Zbl 0925.42016 [5] Cohen, A.; Conze, J. P.: Regularite des bases d’ondelettes et mesures ergodique. Rev. math. Iberoamericana 8, 351-365 (1992) · Zbl 0781.42027 [6] Cohen, A.; Daubechies, I.; Feauveau, J. C.: Biorthogonal bases of compactly supported wavelets. Comm. pure appl. Math. 45, 485-500 (1992) · Zbl 0776.42020 [7] Daubechies, I.: Ten lectures on wavelets. (1992) · Zbl 0776.42018 [8] Daubechies, I.: Orthonormal bases of compactly supported wavelets. Comm. pure appl. Math. 41, 909-996 (1988) · Zbl 0644.42026 [9] Eirola, T.: Sobolev characterization of solution of dilation equations. SIAM J. Math. anal. 23, 1015-1030 (1992) · Zbl 0761.42014 [10] Gopinath, R. A.; Burrus, C. B.: Wavelet transforms and filter banks. (1992) · Zbl 0776.42022 [11] Heller, P. N.: Lagrangemm. (1994) [12] Heller, P. N.: Rankmn. SIAM J. Matrix anal. Appl. 16, 502-519 (1995) [13] Heller, P. N.; Resnikoff, H. L.; Jr., R. O. Wells: Wavelet matrices and the representation of discrete functions. Wavelet: A tutorial in theory and application, 15-50 (1992) · Zbl 0767.15015 [14] Heller, P. N.; Jr., R. O. Wells: The spectral theory of multiresolution operators and applications. Wavelet: theory, algorithm and application, 13-32 (1994) [15] P. N. Heller, R. O. Wells, Jr. Sobolev Regularity for RankM, Computational Math. Laboratory, Rice University, 1996 [16] Herve, L.: Construction et regularite des fonctions d’echelle. SIAM J. Math. anal. 26, 1361-1385 (1995) [17] Huang, D.; Sun, Q.; Zhang, Z.: Integral representation ofm. Chinese sci. Bull. 42, 803-807 (1997) · Zbl 0928.42019 [18] Kautsky, J.: An algebraic construction of discrete wavelet transform. Appl. math. 38, 169-193 (1993) · Zbl 0782.65061 [19] Kautsky, J.; Turkajova, R.: A matrix approach to wavelets. Wavelet: theory, algorithm and application, 117-135 (1994) [20] B. Ma, Q. Sun, Compactly supported refinable distribution in Triebel-Lizorkin spaces and Besov spaces, J. Fourier Anal. Appl. · Zbl 0928.42027 [21] Lewis, R. M.: Cardinal interpolation multiresolution. J. approx. Theory 26, 177-202 (1994) · Zbl 0796.41001 [22] Meyer, Y.: Ondelettes et opérateurs, I: Ondelettes. (1990) · Zbl 0694.41037 [23] Shi, X.; Sun, Q.: A class ofm. Proc. amer. Math. soc. 126, 3501-3506 (1998) · Zbl 0943.42019 [24] Soman, A. K.; Vaidyanathan, P. P.; Nguyen, T. Q.: Linear phase paraunitary filter banks: theory, factorizations and designs. IEEE trans. Signal process. 41, 3480-3496 (1993) · Zbl 0873.93064 [25] Steffen, P.; Heller, P. N.; Gopinath, R. A.; Burrus, C. S.: Theory of regularm. IEEE trans. Signal process. 41, 3497-3511 (1993) · Zbl 0841.94021 [26] Villemoes, L.: Energy moments in time and frequency for two-scale difference equation solutions and wavelets. SIAM J. Math. anal. 23, 1519-1543 (1992) · Zbl 0759.39005 [27] Volker, H.: On the regularity of wavelets. IEEE trans. Signal process. 38, 872-876 (1992) · Zbl 0744.42017 [28] Volker, H.: Asymptotic regularity of compactly supported wavelets. SIAM J. Math. anal. 26, 1075-1087 (1995) · Zbl 0834.42018 [29] Welland, G. V.; Lundberg, M.: Construction of compactp. Constr. approx. 9, 347-370 (1993) · Zbl 0784.42026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.