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1993 | 65 | 1 | 149-156
Tytuł artykułu

Some eigenvalue estimates for wavelet related Toeplitz operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
65
Numer
1
Strony
149-156
Opis fizyczny
Daty
wydano
1993
otrzymano
1993-01-13
Twórcy
  • Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [AFP] J. Arazy, S. Fisher and J. Peetre, Hankel operators on weighted Bergman spaces, Amer. J. Math. 110 (1988), 989-1055.
  • [BS] M. Sh. Birman and M. Z. Solomyak, Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations, Adv. in Soviet Math. 7 (1991), 1-55.
  • [D1] I. Daubechies, Time-frequency localization operators: A geometric phase space approach, IEEE Trans. Inform. Theory 34 (1988), 605-612.
  • [D2] I. Daubechies, The wavelet transform: A method of time-frequency localization, in: Advances in Spectrum Analysis and Array Processing 1, S. Haykin (ed.), Prentice-Hall, New York 1991, 366-417.
  • [DP] I. Daubechies and T. Paul, Time-frequency localization operators - a geometric phase space approach II, the use of dilations, Inverse Problems 4 (1988), 661-680.
  • [FG] H. G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions, J. Funct. Anal. 86 (1989), 307-340.
  • [F] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton University Press, Princeton, N.J., 1989.
  • [JW] S. Janson and T. Wolff, Schatten classes and commutators of singular integral operators, Ark. Mat. 20 (1982), 301-310.
  • [PRW] L. Peng, R. Rochberg and Z. Wu, Orthogonal polynomials and middle Hankel operators on Bergman spaces, Studia Math. 102 (1992), 57-75.
  • [RT] J. Ramanathan and P. Topiwala, Time-frequency localization via the Weyl correspondence, submitted.
  • [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.
  • [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.
  • [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.
  • [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.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv65i1p149bwm
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