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Volumn 3, Issue 6, 1997, Pages 757-774

Stability and Independence of the Shifts of Finitely Many Refinable Functions

Author keywords

(global) linear independence; Matrix refinement mask; Multiresolution; Multiwavelets; Riesz basis; Shift invariant spaces; Stability

Indexed keywords


EID: 1842631015     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02648266     Document Type: Article
Times cited : (15)

References (15)
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    • Regularity of refinable function vectors
    • Cohen, A., Daubechies, I., and Plonka, G. (1997). Regularity of refinable function vectors. J. Fourier Anal. 3, 295-324.
    • (1997) J. Fourier Anal. , vol.3 , pp. 295-324
    • Cohen, A.1    Daubechies, I.2    Plonka, G.3
  • 3
    • 0030560155 scopus 로고    scopus 로고
    • Construction of orthogonal wavelets using fractal interpolation functions
    • Donovan, G.C., Geronimo, J.S., Hardin, D.P., and Massopust, P.R. (1996). Construction of orthogonal wavelets using fractal interpolation functions. SIAM J. Math. Anal. 27, 1791-1815.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1791-1815
    • Donovan, G.C.1    Geronimo, J.S.2    Hardin, D.P.3    Massopust, P.R.4
  • 4
    • 0001544864 scopus 로고
    • Fractal functions and wavelet expansions based on several scaling functions
    • Geronimo, J.S., Hardin, D.P., and Massopust, P.R. (1994). Fractal functions and wavelet expansions based on several scaling functions. J. Approx. Theory 78, 373-401.
    • (1994) J. Approx. Theory , vol.78 , pp. 373-401
    • Geronimo, J.S.1    Hardin, D.P.2    Massopust, P.R.3
  • 7
    • 0000629355 scopus 로고
    • Multiresolution analyses based on fractal functions
    • Hardin, D.P., Kessler, B., and Massopust, P.R. (1992). Multiresolution analyses based on fractal functions. J. Approx. Theory 71, 104-120.
    • (1992) J. Approx. Theory , vol.71 , pp. 104-120
    • Hardin, D.P.1    Kessler, B.2    Massopust, P.R.3
  • 8
    • 1842484437 scopus 로고    scopus 로고
    • Matrix refinement equations: Existence and uniqueness
    • Heil, C. and Colella, D. (1996). Matrix refinement equations: existence and uniqueness. J. Fourier Anal. Appl. 2, 363-377.
    • (1996) J. Fourier Anal. Appl. , vol.2 , pp. 363-377
    • Heil, C.1    Colella, D.2
  • 9
    • 0030526693 scopus 로고    scopus 로고
    • Approximation by translates of refinable functions
    • Heil, C., Strung, G., and Strela, V. (1996). Approximation by translates of refinable functions. Numer. Math. 73, 75-94.
    • (1996) Numer. Math. , vol.73 , pp. 75-94
    • Heil, C.1    Strung, G.2    Strela, V.3
  • 10
    • 0040200717 scopus 로고
    • Stability and independence of the shifts of a multivariate refinable function
    • Hogan, T. ( 1995). Stability and independence of the shifts of a multivariate refinable function. CMS. Techn. Rep. 95-07.
    • (1995) CMS. Techn. Rep. , vol.95 , Issue.7
    • Hogan, T.1
  • 11
    • 84976129526 scopus 로고
    • On linear independence for integer translates of a finite number of functions
    • Jia, R.-Q. and Micchelli, C.A. (1992). On linear independence for integer translates of a finite number of functions. Proc. Edinburgh Math Soc. 36, 69-85.
    • (1992) Proc. Edinburgh Math Soc. , vol.36 , pp. 69-85
    • Jia, R.-Q.1    Micchelli, C.A.2
  • 12
    • 0002888350 scopus 로고
    • Using the refinement equations for the construction of pro-wavelets II: Powers of two
    • (P.-J. Laurent, A. Le Méhauté, and L.L. Schumaker, eds.), Academic Press, New York
    • Jia, R.-Q, and Micchelli, C.A. (1991). Using the refinement equations for the construction of pro-wavelets II: powers of two. in Curves and Surfaces (P.-J. Laurent, A. Le Méhauté, and L.L. Schumaker, eds.), Academic Press, New York, 209-246.
    • (1991) Curves and Surfaces , pp. 209-246
    • Jia, R.-Q.1    Micchelli, C.A.2
  • 13
    • 84966226919 scopus 로고
    • Stability and linear independence associated with wavelet decompositions
    • Jia, R.-Q. and Wang, J. (1993). Stability and linear independence associated with wavelet decompositions. Proc. Amer. Math. Soc. 117, 1115-1124.
    • (1993) Proc. Amer. Math. Soc. , vol.117 , pp. 1115-1124
    • Jia, R.-Q.1    Wang, J.2
  • 14
    • 0031515609 scopus 로고    scopus 로고
    • Approximation order provided by refinable function vectors
    • Plonka, G. (1997). Approximation order provided by refinable function vectors. Constr. Approx. 13, 221-224.
    • (1997) Constr. Approx. , vol.13 , pp. 221-224
    • Plonka, G.1
  • 15
    • 0000423339 scopus 로고
    • Finite element multi wavelets
    • (S.P. Singh, A. Carbone, and B. Watson, eds.), Kluwer, Dordrecht, Netherlands
    • Strung, G. and Strela, V. (1995). Finite element multi wavelets, in Approximation Theory, Wavelets and Applications (S.P. Singh, A. Carbone, and B. Watson, eds.), Kluwer, Dordrecht, Netherlands, 485-496.
    • (1995) Approximation Theory, Wavelets and Applications , pp. 485-496
    • Strung, G.1    Strela, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.