Non-similarity of Walsh and trigonometric systems

P. Wojtaszczyk

Studia Mathematica (2000)

  • Volume: 142, Issue: 2, page 171-185
  • ISSN: 0039-3223

Abstract

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We show that in L p for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.

How to cite

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Wojtaszczyk, P.. "Non-similarity of Walsh and trigonometric systems." Studia Mathematica 142.2 (2000): 171-185. <http://eudml.org/doc/216796>.

@article{Wojtaszczyk2000,
abstract = {We show that in $L_p$ for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.},
author = {Wojtaszczyk, P.},
journal = {Studia Mathematica},
keywords = {Walsh-Paley system; best constants; equivalent bases; Riemann norms},
language = {eng},
number = {2},
pages = {171-185},
title = {Non-similarity of Walsh and trigonometric systems},
url = {http://eudml.org/doc/216796},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Wojtaszczyk, P.
TI - Non-similarity of Walsh and trigonometric systems
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 2
SP - 171
EP - 185
AB - We show that in $L_p$ for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.
LA - eng
KW - Walsh-Paley system; best constants; equivalent bases; Riemann norms
UR - http://eudml.org/doc/216796
ER -

References

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  1. [1] R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer, Berlin, 1993. Zbl0797.41016
  2. [2] D. Jackson, Certain problems in closest approximation, Bull. Amer. Math. Soc. 39 (1933), 889-906. Zbl59.0307.01
  3. [3] A. Pietsch and J. Wenzel, Orthonormal Systems and Banach Space Geometry, Cambridge Univ. Press, Cambridge 1998. Zbl0919.46001
  4. [4] F. Schipp, W. R. Wade and P. Simon, Walsh Series--an Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, Budapest, 1990. Zbl0727.42017
  5. [5] W. S. Young, A note on Walsh-Fourier series, Proc. Amer. Math. Soc. 59 (1976), 305-310. Zbl0335.42010
  6. [6] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Cambridge, 1959. Zbl0085.05601

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