Decompositions of trigonometric polynomials with applications to multivariate subdivision schemes
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Cohen, A., Gröchenig, K., Villemoes, L.F.: Regularity of multivariate refinable functions. Constr. Approx. 15(2), 241–255 (1999)
Cavaretta, A.S., Dahmen, W., Micchelli, C.A.: Stationary subdivision. Mem. Am. Math. Soc. 93(453), vi+186 (1991)
Charina, M.: Vector multivariate subdivisio0n schemes: comparison of spectral methods for their regularity analysis. Appl. Comput. Harmon. Anal. (2011, in press)
Chen, D.-R., Jia, R.-Q., Riemenschneider, S.D.: Convergence of vector subdivision schemes in Sobolev spaces. Appl. Comput. Harmon. Anal. 12(1), 128–149 (2002)
Dyn, N.: Subdivision schemes in computer aided geometric design. In: Light, W. (ed.) Advances in Numerical Analysis, vol. II. Wavelets, Subdivision Algorithms and Radial Basis Functions, pp. 36–104. Clarendon Press, Oxford (1992)
Han, B.: Computing the smoothness exponent of a symmetric multivariate refinable function. SIAM J. Matrix Anal. Appl. 24, 693–714 (2003)
Han, B.: Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix. J. Comput. Appl. Math. 155, 43–67 (2003)
Han, B.: Vector cascade algorithms and refinable function vector in Sobolev spaces. J. Approx. Theory 124, 44–88 (2003)
Han, B., Jia, R.-Q.: Multivariate refinement equations and convergence of subdivision schemes. SIAM J. Math. Anal. 29(5), 1177–1999 (1998)
Latour, V., Müller, J., Nickel, W.: Stationry subdivision for general scaling matrices. Math. Z. 227, 645–661 (1998)
Möller, H.M., Sauer, T.: Multivariate refinable functions of high approximation order via quotient ideals of Laurent polynomials. Adv. Comput. Math. 20(1–3), 205–228 (2004)
Novikov, I.Ya., Protasov, V.Yu., Skopina, M.A.: Wavelet theory. In: Translations Mathematical Monographs, vol. 239. AMS, Providence (2011)
Sauer, T.: How to generate smoother refinable functions from given one In: Haussmann, W., Jetter, K., Reimer, M., Stökler, J. (eds.) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol. 145, pp. 279–294 (2003)
Sauer, T.: Differentiability of multivariate refinable functions and factorization. Adv. Comput. Math. 26(1–3), 211–235 (2006)
Skopina, M.: On construction of multivariate wavelets with vanishing moments. ACHA 20(3), 375–390 (2006)
Wojtaszczyk, P.: A mathematical introduction to wavelets. Lond. Math. Soc. Stud. Texts, vol. 37, xii+261 pp. Cambridge University Press, Cambridge (1997)