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1991 | 100 | 1 | 51-74
Tytuł artykułu

Spaces of sequences, sampling theorem, and functions of exponential type

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EN
Abstrakty
EN
We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called φ-transform studied in [6] [8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces.
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Twórcy
  • Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, U.S.A.
Bibliografia
  • [1] P. Ausscer and M. Carro, On the relations between operators on $ℝ^n$, $𝕋^n$ and $ℤ^n$, Studia Math., to appear.
  • [2] R. Boas, Entire Functions, Academic Press, New York 1954.
  • [3] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
  • [4] K. de Leeuw, On $L^p$ multipliers, Ann. of Math. 81 (1965), 364-379.
  • [5] H. Feichtinger and K. Gröchenig, Banach spaces related to intergrable group representations and their atomic decompositions, I, J. Funct. Anal. 86 (1989), 307-340.
  • [6] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799.
  • [7] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, M. Cwikel et al. (eds.), Lecture Notes in Math. 1302, Springer, 1988, 223-246.
  • [8] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces. J. Funct. Anal., to appear.
  • [9] M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley theory and the study of function spaces, CBMS Regional Conf. Ser. in Math., to appear.
  • [10] M. Frazier and R. Torres, The sampling theorem, φ-transform and Shannon wavelets for R, Z, T and $Z_N$, preprint.
  • [11] C. Heil and D. Walnut, Continuous and discrete wavelet transforms, SIAM Rev. 31 (1989), 628-666.
  • [12] M. Holschneider, Wavelet analysis on the circle, J. Math. Phys. 31 (1990), 39-44.
  • [13] Y. Katznelson, An Introduction to Harmonic Analysis, Dover, New York 1976.
  • [14] S. Mallat, Multiresolution representations and wavelets, Ph.D. Thesis, Electrical Engineering Department, Univ. of Pennsylvania, 1988.
  • [15] Y. Meyer, Wavelets and operators, Proc. of the Special Year in Modern Analysis at the University of Illinois, London Math. Soc. Lecture Note Ser. 137, Cambridge Univ. Press, Cambridge 1989, 256-364.
  • [16] Y. Meyer, Ondelettes et opérateurs, Hermann, Paris 1990.
  • [17] C. Onneweer and S. Weiyi, Homogeneous Besov spaces on locally compact Vilenkin groups, Studia Math. 93 (1989), 17-39.
  • [18] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Durham, N.C., 1976.
  • [19] V. Peller, Wiener-Hopf operators on a finite interval and Schatten-von Neumann classes, Proc. Amer. Math. Soc. 104 (1988), 479-486.
  • [20] B. Petersen, Introduction to the Fourier Transform and Pseudo-differential Operators, Pitman, Boston 1983.
  • [21] R. Rochberg, Toeplitz and Hankel operators on the Paley-Wiener spaces, Integral Equations Operator Theory 10, (1987), 187-235.
  • [22] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
  • [23] R. Torres, Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc. 442 (1991).
  • [24] H. Triebel, Theory of Function Spaces, Monographs Math. 78, Birkhäuser, Basel 1983.
  • [25] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, London 1968.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv100i1p51bwm
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