Convergence behavior of the conjugate Shannon sampling series

Holger Boche

Acta Mathematica et Informatica Universitatis Ostraviensis (1997)

  • Volume: 05, Issue: 1, page 13-26
  • ISSN: 1804-1388

How to cite

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Boche, Holger. "Konvergenzverhalten der konjugierten Shannonschen Abtastreihe." Acta Mathematica et Informatica Universitatis Ostraviensis 05.1 (1997): 13-26. <http://eudml.org/doc/23789>.

@article{Boche1997,
author = {Boche, Holger},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {Shannon sampling series; conjugate function; Sobolev spaces; Hilbert transform},
language = {ger},
number = {1},
pages = {13-26},
publisher = {University of Ostrava},
title = {Konvergenzverhalten der konjugierten Shannonschen Abtastreihe},
url = {http://eudml.org/doc/23789},
volume = {05},
year = {1997},
}

TY - JOUR
AU - Boche, Holger
TI - Konvergenzverhalten der konjugierten Shannonschen Abtastreihe
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 1997
PB - University of Ostrava
VL - 05
IS - 1
SP - 13
EP - 26
LA - ger
KW - Shannon sampling series; conjugate function; Sobolev spaces; Hilbert transform
UR - http://eudml.org/doc/23789
ER -

References

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  1. N. Bary, A treatise on Trigonometrie Series Vol. 2, Pergamon Press LTD, Oxford 1964. (1964) 
  2. P. Butzer R. Nessel, Fourier Analysis and Approximation, Birkhäuser Verlag, New York, 1971. (1971) MR0510857
  3. P. Butzer W. Splettstößer R. Stens, The Sampling Theorem and Linear Prediction in Signal Analysis, Jber. Deutsch. Math.-Vereinigung 90, (1988), S. 1-70. (1988) MR0928745
  4. P. Butzer R. Stens, Sampling Theory for not necessarily band-limited Functions, SIAM Review, March 1992, Vol. 34, No. 1. (1992) MR1156288
  5. P. Butzer W. Splettstösser, Approximation und Interpolation durch verallgemeinerte Abtastsummen, Forschungsbericht No. 2515 des Landes Nordrhein-Westfalen, Köln-Opladen, 1977. (1977) 
  6. P. Butzer, A survey of Whittaker-Shannon sampling theorem and some of its extensions, J. Math. Res. Exposition, 3 (1983), p. 185-212. (1983) MR0724869
  7. L. Carleson, 10.1007/BF02392815, Acta Math. 116, (1966), S. 135-157. (1966) Zbl0144.06402MR0199631DOI10.1007/BF02392815
  8. J. Churkin, C Jakowlew G. Wunsch, Theorie und Anwendung der Signalabtastung, Verlag Technik Berlin, Berlin 1966. (1966) 
  9. A. Jerri, The Shannon sampling theorem - its varios extensions and applications: a tutorial review, Proc. IEEE 65 (1977), 1565-1596. (1977) 
  10. R. J. Marks, Introduction to Shannon Sampling and Interpolation Theory, Sringer Texts in Electrical Engineering, Springer Verlag New York, 1991. (1991) Zbl0729.94001MR1077829
  11. R. J. Marks ed, Advanced Topics in Shannon Sampling and Interpolation Theory, Sringer Texts in Electrical Engineering, Springer Verlag New York, 1993. (1993) Zbl0905.94002MR1221743
  12. H. Triebel, Theory of Function Spaces II, Monographs in Mathematics, Birkhauser Verlag, Basel, 1992. (1992) Zbl0763.46025MR1163193

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