On the localization principle for multi-dimensional Shannon and conjugate Shannon sampling series

Holger Boche

Acta Mathematica et Informatica Universitatis Ostraviensis (1997)

  • Volume: 05, Issue: 1, page 27-37
  • ISSN: 1804-1388

How to cite

top

Boche, Holger. "Über das Lokalisierungsprinzip bei mehrdimensionalen Shannonschen und konjugierten Shannonschen Abtastreihen." Acta Mathematica et Informatica Universitatis Ostraviensis 05.1 (1997): 27-37. <http://eudml.org/doc/23790>.

@article{Boche1997,
author = {Boche, Holger},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {multidimensional Shannon and conjugate Shannon sampling series; Hilbert transform; localization principle; convergence and divergence behaviour},
language = {ger},
number = {1},
pages = {27-37},
publisher = {University of Ostrava},
title = {Über das Lokalisierungsprinzip bei mehrdimensionalen Shannonschen und konjugierten Shannonschen Abtastreihen},
url = {http://eudml.org/doc/23790},
volume = {05},
year = {1997},
}

TY - JOUR
AU - Boche, Holger
TI - Über das Lokalisierungsprinzip bei mehrdimensionalen Shannonschen und konjugierten Shannonschen Abtastreihen
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 1997
PB - University of Ostrava
VL - 05
IS - 1
SP - 27
EP - 37
LA - ger
KW - multidimensional Shannon and conjugate Shannon sampling series; Hilbert transform; localization principle; convergence and divergence behaviour
UR - http://eudml.org/doc/23790
ER -

References

top
  1. H. Boche, Konvergenzverhalten der konjugierten Shannonschen Abtastreihe, accepted in Acta Mathematica et Informatica Universitatis Ostraviensis. Zbl0931.42024
  2. P. Butzer, HASH(0x3011b98), Personliche Mitteilung, RWTH-Aachen, 1995. (1995) Zbl1002.47500
  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, A survey of Whittaker-Shannon sampling theorem and some of its extensions, J. Math. Res. Exposition, 3 (1983), p. 185-212. (1983) MR0724869
  6. D. P. Dryanow, Equiconvergence and equiapproximation for Entire Functions, Constructive Theory of Functions, Varna 91, Sofia 1992, p. 123-136. (1992) 
  7. D. P. Dryanow, On the convergence and saturation problem of a sequence of discrete linear Operators of exponential type in L p ( - , ) Spaces, Acta Math. Hung. 49 (1-2) (1987), p. 103-127. (1987) MR0869666
  8. A. Jerri, The Shannon sampling theorem - its varios extensions and applications: a tutorial review, Proc. IEEE 65 (1977), 1565-1596. (1977) 
  9. R. J. Marks, Introduction to Shannon Sampling and Interpolation Theory, Sringer Texts in Electrical Engineering, Springer Verlag New York, 1991 Zbl0729.94001MR1077829
  10. 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
  11. S. Ries, R. L. Stens, A Localization Principle for the Approximation by Sampling Series, in Proc. Intern. Conf. Theory of Approximation of Functions, Izdat. Nauka, Moscow, 1987, pp. 507-509. (1987) 
  12. R. L. Stens, 10.1016/0165-1684(80)90007-9, Signal Processing 2 (1980), pp. 173-176. (1980) MR0574555DOI10.1016/0165-1684(80)90007-9
  13. R. L. Stens, 10.1016/0165-1684(83)90020-8, Signal Processing 5 (1983), pp. 139-151. (1983) MR0703507DOI10.1016/0165-1684(83)90020-8
  14. R. L. Stens, Approximation of Functions by Whittaker's Cardinal Series, International Series of Numerical Mathematics, Vol. 71, 1984, pp. 137-149. (1984) Zbl0582.42002MR0821793
  15. R. L. Stens, HASH(0x3028860), Personliche Mitteilung, RWTH-Aachen, 1995. (1995) Zbl0835.94004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.