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Volumn 359, Issue 2, 2007, Pages 567-589

Characterizations of function spaces on the sphere using frames

Author keywords

Besov spaces; Nonlinear approximation; Spherical frames; Spherical harmonics; Wavelet decomposition

Indexed keywords


EID: 36249002219     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-06-04030-X     Document Type: Article
Times cited : (20)

References (31)
  • 1
    • 0346494533 scopus 로고    scopus 로고
    • Polynomial wavelet-type expansions on the sphere
    • DOI 10.1023/A:1025016510773
    • A. Askari-Hemmat, M. A. Dehghan, and M. Skopina, Polynomial wavelet-type expansions on the sphere, Math. Notes 74 (2003), no. 2, 292-300. MR2023771 (2005a:42024) (Pubitemid 38103837)
    • (2003) Mathematical Notes , vol.74 , Issue.1-2 , pp. 278-285
    • Askari-Hemmat, A.1    Dehghan, M.A.2    Skopina, M.3
  • 2
    • 0032388665 scopus 로고    scopus 로고
    • Wavelets on the n-sphere and related manifolds
    • DOI 10.1063/1.532481, Wavelet and Time-Frequency Analysis
    • J.P. Antoine and P. Vandergheynst, Wavelets on the n-sphere and related manifolds, J. Math. Phys. 39 (1998), 3987-4008. MR1633175 (99e:42045) (Pubitemid 128113598)
    • (1998) Journal of Mathematical Physics , vol.39 , Issue.8 , pp. 3987-4008
    • Antoine, J.-P.1    Vandergheynst, P.2
  • 3
    • 84967728151 scopus 로고
    • Sommes de Cesaro et multiplicateurs des developpments en harmonique spheriques
    • MR0338697 (49:3461)
    • A. Bonami and J. L. Clerc, Sommes de Cesaro et multiplicateurs des developpments en harmonique spheriques, Trans. Amer. Math. Soc. 183 (1973), 223-263. MR0338697 (49:3461)
    • (1973) Trans. Amer. Math. Soc. , vol.183 , pp. 223-263
    • Bonami, A.1    Clerc, J.L.2
  • 4
    • 13644283759 scopus 로고    scopus 로고
    • Approximation of smooth functions on compact two-point homogeneous spaces
    • DOI 10.1016/j.jfa.2004.10.005, PII S0022123604003489
    • G. Brown and F. Dai, Approximation of smooth functions on compact two-point homogeneous spaces, J. Funct. Anal. 220 (2005), no. 2, 401-423. MR2119285 (2005m:41054) (Pubitemid 40233535)
    • (2005) Journal of Functional Analysis , vol.220 , Issue.2 , pp. 401-423
    • Brown, G.1    Dai, F.2
  • 5
    • 0038051000 scopus 로고
    • Hardy spaces on unit spheres
    • MR0805216 (87d:42031)
    • L. Colzani, Hardy spaces on unit spheres, Boll. Un. Mat. Ital. C(6) 4 (1985), no. 1, 219-244. MR0805216 (87d:42031)
    • (1985) Boll. Un. Mat. Ital. C(6) , vol.4 , Issue.1 , pp. 219-244
    • Colzani, L.1
  • 6
    • 0000044993 scopus 로고
    • Maximal estimates for Cesaro and Riesz means on spheres
    • MR0763947 (86g:43012)
    • L.Colzani, M.H. Taibleson andG.Weiss, Maximal estimates for Cesaro and Riesz means on spheres, Indiana Univ. Math. J. 33 (1984), no. 6, 873-889. MR0763947 (86g:43012)
    • (1984) Indiana Univ. Math. J. , vol.33 , Issue.6 , pp. 873-889
    • Colzani, L.1    Taibleson, M.H.2    Weiss, G.3
  • 8
    • 0001220724 scopus 로고
    • Compression ofwavelet decompositions
    • MR1175690 (94a:42045)
    • R. A. DeVore, B. Jawerth and V. Popov, Compression ofwavelet decompositions, Amer. J. Math. 114 (1992), no. 4, 737-785. MR1175690 (94a:42045)
    • (1992) Amer. J. Math. , vol.114 , Issue.4 , pp. 737-785
    • Devore, R.A.1    Jawerth, B.2    Popov, V.3
  • 9
    • 0001604851 scopus 로고
    • Interpolation spaces and nonlinear approximation
    • Springer-Verlag, New York MR0942269 (89d:41035)
    • R. A. DeVore, V. Popov, Interpolation spaces and nonlinear approximation, Lecture Notes in Mathematics, Vol. 1302, 191-205, Springer-Verlag, New York, 1988. MR0942269 (89d:41035)
    • (1988) Lecture Notes in Mathematics , vol.1302 , pp. 191-205
    • Devore, R.A.1    Popov, V.2
  • 12
    • 0002319407 scopus 로고
    • A discrete transform and decompositions of distribution spaces
    • MR1070037 (92a:46042)
    • M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), no. 1, 34-170. MR1070037 (92a:46042)
    • (1990) J. Funct. Anal. , vol.93 , Issue.1 , pp. 34-170
    • Frazier, M.1    Jawerth, B.2
  • 13
    • 0042285121 scopus 로고    scopus 로고
    • Locally supported wavelets on manifolds with applications to the 2D sphere
    • J. Gottelmann, Locally supported wavelets on manifolds with applications to the 2D sphere, Appl. Comput. Harmon. Anal. 7 (1999), 1-33. MR1699606 (2000j:42051) (Pubitemid 129562936)
    • (1999) Applied and Computational Harmonic Analysis , vol.7 , Issue.1 , pp. 1-33
    • Gottelmann, J.1
  • 14
    • 4644240093 scopus 로고    scopus 로고
    • Harmonic functions on the real hyperbolic ball II Hardy-Sobolev and Lipschitz spaces
    • DOI 10.1002/mana.200310159
    • S. Grellier and P. Jaming, Harmonic functions on the real hyperbolic ball. II. Hardy-Sobolev and Lipschitz spaces, Math. Nachr. 268 (2004), 50-73. MR2054532 (2005a:46067) (Pubitemid 39288685)
    • (2004) Mathematische Nachrichten , vol.268 , pp. 50-73
    • Grellier, S.1    Jaming, P.2
  • 16
    • 21344484691 scopus 로고
    • A bernstein-type inequality associated with wavelet decomposition
    • Wavelets
    • Rong-Qing Jia, A Bernstein-type inequality associated with wavelet decomposition, Con-str. Approx. 9 (1993), 299-318. MR1215774 (94h:41026) (Pubitemid 24805195)
    • (1993) Constructive Approximation , vol.9 , Issue.2-3 , pp. 299
    • Jia, R.-Q.1
  • 17
    • 0030676114 scopus 로고    scopus 로고
    • Compression of functions defined on surfaces of 3D objects
    • March 25-27
    • K. Kolarov and W. Lynch, Compression of functions defined on surfaces of 3D objects, Data Compression Conference (DCC 97), March 25-27 (1997), 281-290.
    • (1997) Data Compression Conference (DCC 97) , pp. 281-290
    • Kolarov, K.1    Lynch, W.2
  • 18
    • 0013512144 scopus 로고
    • Base dondelettes sur les groupes de Lie stratifies (French)
    • MR1015808 (90j:42066)
    • P. G. Lemarie-Rieusset, Base dondelettes sur les groupes de Lie stratifies (French), Bull. Soc. Math. France 117 (1989), no. 2, 211-232. MR1015808 (90j:42066)
    • (1989) Bull. Soc. Math. France , vol.117 , Issue.2 , pp. 211-232
    • Lemarie-Rieusset, P.G.1
  • 19
    • 36248934639 scopus 로고    scopus 로고
    • Polynomial frames: A fast tour, Approximation theory XI: Gatlinburg 2004
    • Nashboro Press, Brentwood, TN MR2126687 (2005k:42087)
    • H. N. Mhaskar and J. Prestin, Polynomial frames: a fast tour, Approximation theory XI: Gatlinburg 2004, 287-318, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2005. MR2126687 (2005k:42087)
    • (2005) Mod. Methods Math. , pp. 287-318
    • Mhaskar, H.N.1    Prestin, J.2
  • 20
    • 0035608775 scopus 로고    scopus 로고
    • Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
    • DOI 10.1090/S0025-5718-00-01240-0
    • H.N. Mhaskar, F.J. Narcowich and J.D. Ward, Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature, Math. Comp. 70 (2001), 1113-1130 (Corrigendum: Math. Comp. 71 (2001) 453-454). MR1710640 (2002a:41032) (Pubitemid 33290484)
    • (2001) Mathematics of Computation , vol.70 , Issue.235 , pp. 1113-1130
    • Mhaskar, H.N.1    Narcowich, F.J.2    Ward, J.D.3
  • 22
    • 0040251195 scopus 로고    scopus 로고
    • Nonstationary wavelets on the m-sphere for scattered data
    • MR1420501 (97h:42020)
    • F. J. Narcowich, J. D. Ward, Nonstationary wavelets on the m-sphere for scattered data, Appl. Comput. Harmon. Anal. 3 (1996), no. 4, 324-336. MR1420501 (97h:42020)
    • (1996) Appl. Comput. Harmon. Anal. , vol.3 , Issue.4 , pp. 324-336
    • Narcowich, F.J.1    Ward, J.D.2
  • 24
    • 0039704504 scopus 로고
    • On the approximation of functions on the sphere
    • MR1252759 (94k:41051)
    • Kh. P. Rustamov, On the approximation of functions on the sphere, Izv. Akad. Nauk SSSR Ser. Mat. 59 (1993), 127-148. MR1252759 (94k:41051)
    • (1993) Izv. Akad. Nauk SSSR Ser. Mat. , vol.59 , pp. 127-148
    • Rustamov, Kh.P.1
  • 26
    • 0003221010 scopus 로고
    • Spherical wavelets: Texture processing
    • Springer-Verlag, Wien, New York
    • P. Schroder and W. Sweldens, Spherical Wavelets: Texture Processing, In P. Hanrahan and W. Purgathofer, editors, Rendering Techniques 95, pp. 252-263, Springer-Verlag, Wien, New York, 1995.
    • (1995) Rendering Techniques , vol.95 , pp. 252-263
    • Schroder, P.1    Sweldens, W.2
  • 28
    • 0000902189 scopus 로고
    • Multipliers for spherical harmonic expansions
    • MR0306823 (46:5945)
    • R. Strichartz, Multipliers for spherical harmonic expansions, Trans. Amer. Math. Soc. 167 (1972), 115-124. MR0306823 (46:5945)
    • (1972) Trans. Amer. Math. Soc. , vol.167 , pp. 115-124
    • Strichartz, R.1
  • 30
    • 0009270747 scopus 로고    scopus 로고
    • The best m-term approximation and greedy algorithms
    • V. N. Temlyakov, The best m-term approximation and greedy algorithms, Adv. Comput. Math. 8 (1998), no. 3, 249-265. MR1628182 (99f:41037) (Pubitemid 128695535)
    • (1998) Advances in Computational Mathematics , vol.8 , Issue.3 , pp. 249-265
    • Temlyakov, V.N.1
  • 31
    • 21144435474 scopus 로고    scopus 로고
    • Nonlinear methods of approximation
    • DOI 10.1007/s102080010029
    • V. N. Temlyakov, Nonlinear methods of approximation, Found. Comput. Math. 3 (2003), no. 1, 33-107. MR1951502 (2003j:41029) (Pubitemid 36256890)
    • (2003) Found. Comput. Math. , vol.3 , Issue.1 , pp. 33-107
    • Temlyakov, V.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.