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Volumn 15, Issue 1, 2009, Pages 1-30

Multivariate symmetric interpolating scaling vectors with duals

Author keywords

Biorthogonal basis; Expanding scaling matrix; Interpolating scaling vector; Multiwavelet

Indexed keywords


EID: 59749088564     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-008-9053-x     Document Type: Article
Times cited : (7)

References (44)
  • 1
    • 0003030394 scopus 로고    scopus 로고
    • Accuracy of lattice translates of several multidimensional refinable functions
    • C. Cabrelli C. Heil U. Molter 1998 Accuracy of lattice translates of several multidimensional refinable functions J. Approx. Theory 95 5 52
    • (1998) J. Approx. Theory , vol.95 , pp. 5-52
    • Cabrelli, C.1    Heil, C.2    Molter, U.3
  • 2
    • 23044522973 scopus 로고    scopus 로고
    • Accuracy of several multidimensional refinable distributions
    • C. Cabrelli C. Heil U. Molter 2000 Accuracy of several multidimensional refinable distributions J. Fourier Anal. Appl. 6 5 483 502
    • (2000) J. Fourier Anal. Appl. , vol.6 , Issue.5 , pp. 483-502
    • Cabrelli, C.1    Heil, C.2    Molter, U.3
  • 3
    • 2642532926 scopus 로고    scopus 로고
    • Self-similarity and multiwavelets in higher dimensions
    • C. Cabrelli C. Heil U. Molter 2004 Self-similarity and multiwavelets in higher dimensions Mem. Am. Math. Soc. 170 807 82
    • (2004) Mem. Am. Math. Soc. , vol.170 , Issue.807 , pp. 82
    • Cabrelli, C.1    Heil, C.2    Molter, U.3
  • 7
    • 27844453239 scopus 로고    scopus 로고
    • Matrix-valued symmetric templates for interpolatory surface subdivisions: I. Regular vertices
    • C.K. Chui Q.T. Jiang 2005 Matrix-valued symmetric templates for interpolatory surface subdivisions: I. Regular vertices Appl. Comput. Harmon. Anal. 19 3 303 339
    • (2005) Appl. Comput. Harmon. Anal. , vol.19 , Issue.3 , pp. 303-339
    • Chui, C.K.1    Jiang, Q.T.2
  • 8
    • 0028494805 scopus 로고
    • A general framework of multivariate wavelets with duals
    • C.K. Chui C. Li 1994 A general framework of multivariate wavelets with duals Appl. Comput. Harmon. Anal. 1 4 368 390
    • (1994) Appl. Comput. Harmon. Anal. , vol.1 , Issue.4 , pp. 368-390
    • Chui, C.K.1    Li, C.2
  • 9
    • 0002118102 scopus 로고
    • Non-separable bidimensional wavelet bases
    • A. Cohen I. Daubechies 1993 Non-separable bidimensional wavelet bases Rev. Mat. Iberoam. 9 51 137
    • (1993) Rev. Mat. Iberoam. , vol.9 , pp. 51-137
    • Cohen, A.1    Daubechies, I.2
  • 10
    • 1842558556 scopus 로고    scopus 로고
    • Interpolatory rank-1 vector subdivision schemes
    • C. Conti G. Zimmermann 2004 Interpolatory rank-1 vector subdivision schemes Comput. Aided Geom. Des. 21 4 341 351
    • (2004) Comput. Aided Geom. Des. , vol.21 , Issue.4 , pp. 341-351
    • Conti, C.1    Zimmermann, G.2
  • 11
    • 0038571618 scopus 로고    scopus 로고
    • A new approach to interpolating scaling functions
    • S. Dahlke K.-H. Gröchenig P. Maass 1999 A new approach to interpolating scaling functions Appl. Anal. 72 3-4 485 500
    • (1999) Appl. Anal. , vol.72 , Issue.34 , pp. 485-500
    • Dahlke, S.1    Gröchenig, K.-H.2    Maass, P.3
  • 12
    • 0031191702 scopus 로고    scopus 로고
    • Interpolating refinable functions and wavelets for general scaling matrices
    • S. Dahlke P. Maass 1997 Interpolating refinable functions and wavelets for general scaling matrices Numer. Funct. Anal. Optim. 18 5-6 521 539
    • (1997) Numer. Funct. Anal. Optim. , vol.18 , Issue.56 , pp. 521-539
    • Dahlke, S.1    Maass, P.2
  • 14
    • 0027574359 scopus 로고
    • Using the refinement equation for evaluating integrals of wavelets
    • W. Dahmen C.A. Micchelli 1993 Using the refinement equation for evaluating integrals of wavelets SIAM J. Numer. Anal. 30 2 507 537
    • (1993) SIAM J. Numer. Anal. , vol.30 , Issue.2 , pp. 507-537
    • Dahmen, W.1    Micchelli, C.A.2
  • 16
  • 17
    • 0035277292 scopus 로고    scopus 로고
    • Nonseparable, compactly supported interpolating refinable functions with arbitrary smoothness
    • J. Derado 2001 Nonseparable, compactly supported interpolating refinable functions with arbitrary smoothness Appl. Comput. Harmon. Anal. 10 2 113 138
    • (2001) Appl. Comput. Harmon. Anal. , vol.10 , Issue.2 , pp. 113-138
    • Derado, J.1
  • 18
    • 0001406484 scopus 로고
    • Multidimensional iterative interpolation
    • G. Deslauriers J. Dubois S. Dubuc 1991 Multidimensional iterative interpolation Can. J. Math. 43 43 297 312
    • (1991) Can. J. Math. , vol.43 , Issue.43 , pp. 297-312
    • Deslauriers, G.1    Dubois, J.2    Dubuc, S.3
  • 19
    • 0041407181 scopus 로고    scopus 로고
    • Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets
    • B. Han 2001 Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets J. Approx. Theory 110 1 18 53
    • (2001) J. Approx. Theory , vol.110 , Issue.1 , pp. 18-53
    • Han, B.1
  • 20
    • 31244436552 scopus 로고    scopus 로고
    • Symmetry property and construction of wavelets with a general dilation matrix
    • B. Han 2002 Symmetry property and construction of wavelets with a general dilation matrix Linear Algebra Appl. 353 1-3 207 225
    • (2002) Linear Algebra Appl. , vol.353 , Issue.13 , pp. 207-225
    • Han, B.1
  • 21
    • 0242508421 scopus 로고    scopus 로고
    • Vector cascade algorithms and refinable function vectors in Sobolev spaces
    • B. Han 2003 Vector cascade algorithms and refinable function vectors in Sobolev spaces J. Approx. Theory 124 1 44 88
    • (2003) J. Approx. Theory , vol.124 , Issue.1 , pp. 44-88
    • Han, B.1
  • 22
    • 6344238953 scopus 로고    scopus 로고
    • Symmetric multivariate orthogonal refinable functions
    • B. Han 2004 Symmetric multivariate orthogonal refinable functions Appl. Comput. Harmon. Anal. 17 3 277 292
    • (2004) Appl. Comput. Harmon. Anal. , vol.17 , Issue.3 , pp. 277-292
    • Han, B.1
  • 23
    • 0000043776 scopus 로고    scopus 로고
    • Optimal interpolatory subdivision schemes in multidimensional spaces
    • B. Han R.-Q. Jia 1998 Optimal interpolatory subdivision schemes in multidimensional spaces SIAM J. Numer. Anal. 36 105 124
    • (1998) SIAM J. Numer. Anal. , vol.36 , pp. 105-124
    • Han, B.1    Jia, R.-Q.2
  • 24
    • 0036003389 scopus 로고    scopus 로고
    • Quincunx fundamental refinable functions and quincunx biorthogonal wavelets
    • B. Han R.-Q. Jia 2002 Quincunx fundamental refinable functions and quincunx biorthogonal wavelets Math. Comput. 71 237 165 196
    • (2002) Math. Comput. , vol.71 , Issue.237 , pp. 165-196
    • Han, B.1    Jia, R.-Q.2
  • 25
    • 5644297306 scopus 로고    scopus 로고
    • Multivariate refinable Hermite interpolants
    • B. Han B. Piper P.-Y. Yu 2004 Multivariate refinable Hermite interpolants Math. Comput. 73 248 1913 1935
    • (2004) Math. Comput. , vol.73 , Issue.248 , pp. 1913-1935
    • Han, B.1    Piper, B.2    Yu, P.-Y.3
  • 26
    • 0011461344 scopus 로고    scopus 로고
    • Multivariate compactly supported fundamental refinable functions, duals, and biorthogonal wavelets
    • H. Ji S.D. Riemenschneider Z. Shen 1999 Multivariate compactly supported fundamental refinable functions, duals, and biorthogonal wavelets Stud. Appl. Math. 102 2 173 204
    • (1999) Stud. Appl. Math. , vol.102 , Issue.2 , pp. 173-204
    • Ji, H.1    Riemenschneider, S.D.2    Shen, Z.3
  • 27
    • 0032441174 scopus 로고    scopus 로고
    • Shift-invariant spaces and linear operator equations
    • R.Q. Jia 1998 Shift-invariant spaces and linear operator equations Isr. J. Math. 103 259 288
    • (1998) Isr. J. Math. , vol.103 , pp. 259-288
    • Jia, R.Q.1
  • 28
    • 0142200354 scopus 로고    scopus 로고
    • Spectral analysis of the transition operator and its applications to smoothness analysis of wavelets
    • R.Q. Jia Q.T. Jiang 2003 Spectral analysis of the transition operator and its applications to smoothness analysis of wavelets SIAM J. Matrix Anal. Appl. 24 4 1071 1109
    • (2003) SIAM J. Matrix Anal. Appl. , vol.24 , Issue.4 , pp. 1071-1109
    • Jia, R.Q.1    Jiang, Q.T.2
  • 29
    • 84976129526 scopus 로고
    • On linear independence for integer translates of a finite number of functions
    • R.Q. Jia C.A. Micchelli 1992 On linear independence for integer translates of a finite number of functions Proc. Edinb. Math. Soc. 36 69 85
    • (1992) Proc. Edinb. Math. Soc. , vol.36 , pp. 69-85
    • Jia, R.Q.1    Micchelli, C.A.2
  • 31
    • 0001730758 scopus 로고    scopus 로고
    • Multivariate matrix refinable functions with arbitrary matrix dilation
    • Q.T. Jiang 1999 Multivariate matrix refinable functions with arbitrary matrix dilation Trans. Am. Math. Soc. 351 2407 2438
    • (1999) Trans. Am. Math. Soc. , vol.351 , pp. 2407-2438
    • Jiang, Q.T.1
  • 34
    • 62949214366 scopus 로고    scopus 로고
    • Logos Berlin
    • d. Logos, Berlin (2007)
    • (2007) D
    • Koch, K.1
  • 35
    • 33846688937 scopus 로고    scopus 로고
    • Multivariate orthonormal interpolating scaling vectors
    • K. Koch 2007 Multivariate orthonormal interpolating scaling vectors Appl. Comput. Harmon. Anal. 22 2 198 216
    • (2007) Appl. Comput. Harmon. Anal. , vol.22 , Issue.2 , pp. 198-216
    • Koch, K.1
  • 36
    • 0003219253 scopus 로고    scopus 로고
    • Balanced multiwavelets: Theory and design
    • J. Lebrun M. Vetterli 1998 Balanced multiwavelets: Theory and design IEEE Trans. Signal Process. 46 4 1119 1125
    • (1998) IEEE Trans. Signal Process. , vol.46 , Issue.4 , pp. 1119-1125
    • Lebrun, J.1    Vetterli, M.2
  • 37
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • J.A. Nelder R. Mead 1965 A simplex method for function minimization Comput. J. 7 308 313
    • (1965) Comput. J. , vol.7 , pp. 308-313
    • Nelder, J.A.1    Mead, R.2
  • 38
    • 0001008029 scopus 로고
    • An efficient method for finding the minimum of a function of several variables without calculating derivatives
    • M.J.D. Powell 1964 An efficient method for finding the minimum of a function of several variables without calculating derivatives Comput. J. 7 155 162
    • (1964) Comput. J. , vol.7 , pp. 155-162
    • Powell, M.J.D.1
  • 39
    • 0001281985 scopus 로고    scopus 로고
    • Multidimensional interpolatory subdivision schemes
    • S.D. Riemenschneider Z. Shen 1997 Multidimensional interpolatory subdivision schemes SIAM J. Numer. Anal. 34 6 2357 2381
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.6 , pp. 2357-2381
    • Riemenschneider, S.D.1    Shen, Z.2
  • 40
    • 0033346489 scopus 로고    scopus 로고
    • d ) II
    • Aldroubi, A., Laine, A., Unser, M., (eds.) Wavelet Applications in Signal and Image Processing VII
    • d ) II. In: Aldroubi, A., Laine, A., Unser, M., (eds.) Wavelet Applications in Signal and Image Processing VII. Proceedings of the SPIEE, vol. 3813, pp. 264-272 (1999)
    • (1999) Proceedings of the SPIEE , vol.3813 , pp. 264-272
    • Riemenschneider, S.D.1    Shen, Z.2
  • 42
    • 0032632455 scopus 로고    scopus 로고
    • Interpolating multiwavelet bases and the sampling theorem
    • I.W. Selesnick 1999 Interpolating multiwavelet bases and the sampling theorem IEEE Trans. Signal Process. 47 6 1615 1621
    • (1999) IEEE Trans. Signal Process. , vol.47 , Issue.6 , pp. 1615-1621
    • Selesnick, I.W.1
  • 44
    • 0027853485 scopus 로고
    • On sampling theorem, wavelets and wavelet transforms
    • X.-G. Xia Z. Zhang 1993 On sampling theorem, wavelets and wavelet transforms IEEE Trans. Signal Process. 41 12 3524 3535
    • (1993) IEEE Trans. Signal Process. , vol.41 , Issue.12 , pp. 3524-3535
    • Xia, X.-G.1    Zhang, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.