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Volumn 43, Issue 6, 2006, Pages 2500-2516

Localization of the generalized sampling series and its numerical application

Author keywords

Error estimate; Gaussian; Generalized sampling series; Localization; Meyer wavelets

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS;

EID: 33845529636     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/04061845X     Document Type: Article
Times cited : (15)

References (33)
  • 2
    • 0001693842 scopus 로고
    • On the functions which are represented by the expansion of the interpolation theory
    • E. T. WHITTAKER, On the functions which are represented by the expansion of the interpolation theory, Proc. Roy. Soc. Edinburgh Sect. A, 35 (1915), pp. 181-194.
    • (1915) Proc. Roy. Soc. Edinburgh Sect. A , vol.35 , pp. 181-194
    • Whittaker, E.T.1
  • 3
    • 0342623858 scopus 로고
    • On the carrying capacity of the "ether" and wire in telecommunications, material for the first all-union conference on questions of communications
    • Moscow, (in Russian)
    • V. KOTEL'NIKOV, On the carrying capacity of the "ether" and wire in telecommunications, material for the first All-Union Conference on Questions of Communications, Izd. Red. Upr. Svyazi RKKA, Moscow, 1933 (in Russian).
    • (1933) Izd. Red. Upr. Svyazi RKKA
    • Kotel'nikov, V.1
  • 4
    • 84911837213 scopus 로고
    • Communications in the presence of noise
    • C. E. SHANNON, Communications in the presence of noise, Proc. I.R.E., 37 (1949), pp. 10-21.
    • (1949) Proc. I.R.E. , vol.37 , pp. 10-21
    • Shannon, C.E.1
  • 9
    • 0010815554 scopus 로고
    • Über eine interpolationsformel von de la vallée poussin
    • M. THEIS, Über eine Interpolationsformel von de la Vallée Poussin, Math. Z., 3 (1919), pp. 93-113.
    • (1919) Math. Z. , vol.3 , pp. 93-113
    • Theis, M.1
  • 10
    • 0000151183 scopus 로고
    • Truncation error of sampling-theorem expansions
    • H. D. HELMS AND J. B. THOMAS, Truncation error of sampling-theorem expansions, Proc. I.R.E., 50 (1962), pp. 179-184.
    • (1962) Proc. I.R.E. , vol.50 , pp. 179-184
    • Helms, H.D.1    Thomas, J.B.2
  • 11
    • 0000003735 scopus 로고
    • Bounds for truncation error of the sampling expansion
    • D. JAGERMAN, Bounds for truncation error of the sampling expansion, SIAM J. Appl. Math., 14 (1966), pp. 714-723.
    • (1966) SIAM J. Appl. Math. , vol.14 , pp. 714-723
    • Jagerman, D.1
  • 12
    • 0001152466 scopus 로고
    • Sampling theorem for the Fourier transform of a distribution with bounded support
    • L. L. CAMPBELL, Sampling theorem for the Fourier transform of a distribution with bounded support, SIAM J. Appl. Math., 16 (1968), pp. 626-636.
    • (1968) SIAM J. Appl. Math. , vol.16 , pp. 626-636
    • Campbell, L.L.1
  • 13
    • 0005710311 scopus 로고
    • Approximate interpolation and the sampling theorem
    • A. J. LEE, Approximate interpolation and the sampling theorem, SIAM J. Appl. Math., 32 (1977), pp. 731-744.
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 731-744
    • Lee, A.J.1
  • 15
    • 0012804049 scopus 로고
    • A modification of the Whittaker-Kotel'nikov-Shannon sampling series
    • P. L. BUTZER AND R. L. STENS, A modification of the Whittaker- Kotel'nikov-Shannon sampling series, Aequationes Math., 28 (1985), pp. 305-311.
    • (1985) Aequationes Math. , vol.28 , pp. 305-311
    • Butzer, P.L.1    Stens, R.L.2
  • 16
    • 0032562315 scopus 로고    scopus 로고
    • Shannon-Gabor wavelet distributed approximating functional
    • D. K. HOFFMAN, G. W. WEI, D. S. ZHANG, AND D. J. KOURI, Shannon-Gabor wavelet distributed approximating functional, Chem. Phys. Letters, 287 (1998), pp. 119-124.
    • (1998) Chem. Phys. Letters , vol.287 , pp. 119-124
    • Hoffman, D.K.1    Wei, G.W.2    Zhang, D.S.3    Kouri, D.J.4
  • 18
    • 0000338940 scopus 로고
    • Irregular sampling theorems and series expansions of band-limited functions
    • H. G. FEICHTINGER AND K. GRÖCHENIG, Irregular sampling theorems and series expansions of band-limited functions, J. Math. Anal. Appl., 167 (1992), pp. 530-556.
    • (1992) J. Math. Anal. Appl. , vol.167 , pp. 530-556
    • Feichtinger, H.G.1    Gröchenig, K.2
  • 21
    • 16244405652 scopus 로고    scopus 로고
    • Hypercircle inequalities and sampling theory
    • A. G. GARCÍA AND A. PORTAL, Hypercircle inequalities and sampling theory, Appl. Anal., 82 (2003), pp. 1111-1125.
    • (2003) Appl. Anal. , vol.82 , pp. 1111-1125
    • García, A.G.1    Portal, A.2
  • 22
    • 0037383937 scopus 로고    scopus 로고
    • On the regularized WKS sampling formula
    • L. W. QIAN, On the regularized WKS sampling formula, Proc. Amer. Math. Soc., 131 (2003), pp. 1169-1176.
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 1169-1176
    • Qian, L.W.1
  • 23
    • 33646595634 scopus 로고    scopus 로고
    • A modification of the sampling series with a Gaussian multiplier
    • to appear
    • L. W. QIAN AND D. B. CREAMER, A modification of the sampling series with a Gaussian multiplier, Samp. Theory Signal Image Process, to appear.
    • Samp. Theory Signal Image Process
    • Qian, L.W.1    Creamer, D.B.2
  • 25
    • 33845548790 scopus 로고    scopus 로고
    • Modified sinc kernels for the localized sampling series
    • L. W. QIAN AND H. OGAWA, Modified sinc kernels for the localized sampling series, Samp. Theory Signal Image Process., 4 (2005), pp. 121-139.
    • (2005) Samp. Theory Signal Image Process. , vol.4 , pp. 121-139
    • Qian, L.W.1    Ogawa, H.2
  • 26
    • 0000795691 scopus 로고
    • An order of convergence for some radial functions
    • I. R. H. JACKSON, An order of convergence for some radial functions, IMA J. Numer. Anal., 9 (1989), pp. 567-587.
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 567-587
    • Jackson, I.R.H.1
  • 27
    • 34248654235 scopus 로고    scopus 로고
    • Generalized de la Vallée Poussin kernel and its numerical application
    • submitted
    • L. W. QIAN AND D. B. CREAMER, Generalized de la Vallée Poussin kernel and its numerical application, Appl. Numer. Math., submitted.
    • Appl. Numer. Math.
    • Qian, L.W.1    Creamer, D.B.2
  • 31
    • 0026624017 scopus 로고
    • A sampling theorem for wavelet subspaces
    • G. G. WALTER, A sampling theorem for wavelet subspaces, IEEE Trans. Inform. Theory, 38 (1992), pp. 881-884.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 881-884
    • Walter, G.G.1
  • 32
    • 0012234662 scopus 로고    scopus 로고
    • Truncation error on wavelet sampling expansions
    • N. ATREAS AND C. KARANIKAS, Truncation error on wavelet sampling expansions, J. Comput. Anal. Appl., 2 (2000), pp. 89-102.
    • (2000) J. Comput. Anal. Appl. , vol.2 , pp. 89-102
    • Atreas, N.1    Karanikas, C.2
  • 33
    • 0009218104 scopus 로고    scopus 로고
    • A quadrature formula based on sampling in Meyer wavelet subspaces
    • X. P. SHEN, A quadrature formula based on sampling in Meyer wavelet subspaces, J. Comput. Anal. Appl., 3 (2001), pp. 147-163.
    • (2001) J. Comput. Anal. Appl. , vol.3 , pp. 147-163
    • Shen, X.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.