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Volumn 23, Issue 3, 2006, Pages 325-350

Function spaces in lipschitz domains and optimal rates of convergence for sampling

Author keywords

Approximation numbers; Function spaces on Lipschitz domains; Rate of convergence; Sampling numbers

Indexed keywords


EID: 32944467038     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00365-005-0612-y     Document Type: Article
Times cited : (65)

References (23)
  • 1
    • 0034381734 scopus 로고    scopus 로고
    • High-dimensional polynomial interpolation on sparse grids
    • V. BARTHELMANN, E. NOVAK, K. RITTER (1999): High-dimensional polynomial interpolation on sparse grids. Adv. Comput. Math., 12:273-288.
    • (1999) Adv. Comput. Math. , vol.12 , pp. 273-288
    • Barthelmann, V.1    Novak, E.2    Ritter, K.3
  • 2
    • 0039496348 scopus 로고    scopus 로고
    • About approximation numbers in function spaces
    • A. M. CAETANO (1998): About approximation numbers in function spaces. J. Approx. Theory, 94:383-395.
    • (1998) J. Approx. Theory , vol.94 , pp. 383-395
    • Caetano, A.M.1
  • 5
    • 0242510921 scopus 로고    scopus 로고
    • Intrinsic characterizations of Besov spaces on Lipschitz domains
    • S. DISPA (2003): Intrinsic characterizations of Besov spaces on Lipschitz domains. Math. Nachr., 260:21-33.
    • (2003) Math. Nachr. , vol.260 , pp. 21-33
    • Dispa, S.1
  • 7
    • 18144381929 scopus 로고    scopus 로고
    • Approximation of anisotropic Besov classes of functions by standard information
    • G. FANG, F. J. HICKERNELL, H. LI (2005): Approximation of anisotropic Besov classes of functions by standard information. J. Complexity, 21:294-313.
    • (2005) J. Complexity , vol.21 , pp. 294-313
    • Fang, G.1    Hickernell, F.J.2    Li, H.3
  • 8
    • 38249008431 scopus 로고
    • Lower bounds for the complexity of Monte Carlo function approximation
    • S. HEINRICH (1992): Lower bounds for the complexity of Monte Carlo function approximation. J. Complexity, 8:277-300.
    • (1992) J. Complexity , vol.8 , pp. 277-300
    • Heinrich, S.1
  • 9
    • 0001015105 scopus 로고
    • Random approximation in numerical analysis
    • (Bierstedt, K. D. et al., eds.). Proc. Essen Conf. 1991. New York: Dekker
    • S. HEINRICH (1994): Random approximation in numerical analysis. In: Functional Analysis (Bierstedt, K. D. et al., eds.). Proc. Essen Conf. 1991. New York: Dekker, pp. 123-171.
    • (1994) Functional Analysis , pp. 123-171
    • Heinrich, S.1
  • 10
    • 1242277383 scopus 로고    scopus 로고
    • Quantum approximation II: Sobolev embeddings
    • S. HEINRICH (2004): Quantum approximation II: Sobolev embeddings. J. Complexity, 20:27-45.
    • (2004) J. Complexity , vol.20 , pp. 27-45
    • Heinrich, S.1
  • 11
    • 22044433640 scopus 로고    scopus 로고
    • The best accuracy of reconstruction of finitely smooth functions from their values at a given number of points
    • S. N. KUDRYAVTSEV (1998): The best accuracy of reconstruction of finitely smooth functions from their values at a given number of points. Izv. Math., 62(1): 19-53.
    • (1998) Izv. Math. , vol.62 , Issue.1 , pp. 19-53
    • Kudryavtsev, S.N.1
  • 12
    • 0003211763 scopus 로고
    • Deterministic and stochastic error bounds in mumerical analysis
    • Berlin: Springer-Verlag
    • E. NOVAK (1988): Deterministic and Stochastic Error Bounds in Mumerical Analysis. Lecture Notes in Mathematics, Vol. 1349. Berlin: Springer-Verlag.
    • (1988) Lecture Notes in Mathematics , vol.1349
    • Novak, E.1
  • 13
    • 0040036758 scopus 로고    scopus 로고
    • On restrictions and extensions of the Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains
    • V. S. RYCHKOV (1999): On restrictions and extensions of the Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains. J. London Math. Soc., 60:237-257.
    • (1999) J. London Math. Soc. , vol.60 , pp. 237-257
    • Rychkov, V.S.1
  • 21
    • 0042420166 scopus 로고    scopus 로고
    • Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers
    • H. TRIEBEL (2002): Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers. Rev. Mat. Comput., 15:475-524.
    • (2002) Rev. Mat. Comput. , vol.15 , pp. 475-524
    • Triebel, H.1
  • 22
    • 11144293601 scopus 로고    scopus 로고
    • Finite order weights imply tractability of linear multivariate problems
    • G. W. WASILKOWSKI, H. WOŹNIAKOWSKI (2004): Finite order weights imply tractability of linear multivariate problems. J. Approx. Theory, 130:57-77.
    • (2004) J. Approx. Theory , vol.130 , pp. 57-77
    • Wasilkowski, G.W.1    Woźniakowski, H.2
  • 23
    • 0035529775 scopus 로고    scopus 로고
    • Local polynomial reproduction and moving least squares approximation
    • H. WENDLAND (2001): Local polynomial reproduction and moving least squares approximation. IMA J. Numer. Anal., 21:285-300.
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 285-300
    • Wendland, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.