Some eigenvalue estimates for wavelet related Toeplitz operators

Krzysztof Nowak

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 1, page 149-156
  • ISSN: 0010-1354

Abstract

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By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end of the second section we include some comments about the range of applicability of our estimates.

How to cite

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Nowak, Krzysztof. "Some eigenvalue estimates for wavelet related Toeplitz operators." Colloquium Mathematicae 65.1 (1993): 149-156. <http://eudml.org/doc/210199>.

@article{Nowak1993,
abstract = {By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end of the second section we include some comments about the range of applicability of our estimates.},
author = {Nowak, Krzysztof},
journal = {Colloquium Mathematicae},
keywords = {Schrödinger representation; eigenvalue estimates; Toeplitz operators; eigenvalue estimates for Toeplitz operators; reproducing formulas; wavelet theory; Calderón-Toeplitz operators},
language = {eng},
number = {1},
pages = {149-156},
title = {Some eigenvalue estimates for wavelet related Toeplitz operators},
url = {http://eudml.org/doc/210199},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Nowak, Krzysztof
TI - Some eigenvalue estimates for wavelet related Toeplitz operators
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 1
SP - 149
EP - 156
AB - By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end of the second section we include some comments about the range of applicability of our estimates.
LA - eng
KW - Schrödinger representation; eigenvalue estimates; Toeplitz operators; eigenvalue estimates for Toeplitz operators; reproducing formulas; wavelet theory; Calderón-Toeplitz operators
UR - http://eudml.org/doc/210199
ER -

References

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  3. [D1] I. Daubechies, Time-frequency localization operators: A geometric phase space approach, IEEE Trans. Inform. Theory 34 (1988), 605-612. Zbl0672.42007
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  10. [RT] J. Ramanathan and P. Topiwala, Time-frequency localization via the Weyl correspondence, submitted. Zbl0787.94003
  11. [R1] R. Rochberg, Toeplitz and Hankel operators, wavelets, NWO sequences, and almost diagonalization of operators, in: Operator Theory: Operator Algebras and Applications, W. B. Arveson and R. G. Douglas (eds.), Proc. Sympos. Pure Math. 51, Part 1, Amer. Math. Soc., 1990, 425-444. 
  12. [R2] R. Rochberg, Eigenvalue estimates for Calderón-Toeplitz operators, in: Function Spaces, K. Jarosz (ed.), Lecture Notes in Pure and Appl. Math. 136, Dekker, 1992, 345-357. 
  13. [RS] R. Rochberg and S. Semmes, End point results for estimates of singular values of integral operators, in: Contributions to Operator Theory and its Applications, I. Gohberg et al. (eds.), Oper. Theory: Adv. Appl. 35, Birkhäuser, Boston 1988, 217-231. 
  14. [S] K. Seip, Mean value theorems and concentration operators in Bargmann and Bergman spaces, in: Wavelets, J. M. Combes, A. Grossmann and Ph. Tchami- tchian (eds.), Springer, Berlin 1989, 209-215. Zbl0850.46012

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