On truncated Wiener-Hopf operators and $BMO(\mathbb {Z})$
HTML articles powered by AMS MathViewer
- by Marcus Carlsson
- Proc. Amer. Math. Soc. 139 (2011), 1717-1733
- DOI: https://doi.org/10.1090/S0002-9939-2010-10598-1
- Published electronically: November 5, 2010
- PDF | Request permission
Abstract:
We give a tractable estimate for the norm of a truncated Wiener-Hopf operator in terms of the discrete $BMO$-space. We also improve earlier norm estimates as well as obtain new, more tractable, criteria for compactness.References
- Andersson, F., Carlsson, M., de Hoop, M., Sparse approximation of functions using sums of exponentials. Preprint.
- MihĂĄly Bakonyi and Dan Timotin, On an extension problem for polynomials, Bull. London Math. Soc. 33 (2001), no. 5, 599â605. MR 1844558, DOI 10.1112/S0024609301008268
- Baranov, A., Chalendar, I., Fricain, E., Mashreghi, J., Timotin, D., Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators, Journal of Funct. Anal. 259 (2010), no. 10, 2673â2701.
- Donald L. Cohn, Measure theory, BirkhÀuser, Boston, Mass., 1980. MR 578344
- Robert L. Ellis and Israel Gohberg, Orthogonal systems and convolution operators, Operator Theory: Advances and Applications, vol. 140, BirkhÀuser Verlag, Basel, 2003. MR 1942683, DOI 10.1007/978-3-0348-8045-9
- Lawrence C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 1998. MR 1625845, DOI 10.1090/gsm/019
- L. N. NikolâČskaya and Yu. B. Farforovskaya, Toeplitz and Hankel matrices as Hadamard-Schur multipliers, Algebra i Analiz 15 (2003), no. 6, 141â160 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 15 (2004), no. 6, 915â928. MR 2044634, DOI 10.1090/S1061-0022-04-00838-6
- Israel Gohberg, Seymour Goldberg, and Marinus A. Kaashoek, Classes of linear operators. Vol. I, Operator Theory: Advances and Applications, vol. 49, BirkhÀuser Verlag, Basel, 1990. MR 1130394, DOI 10.1007/978-3-0348-7509-7
- Lars Hörmander, The analysis of linear partial differential operators. I, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1990. Distribution theory and Fourier analysis. MR 1065993, DOI 10.1007/978-3-642-61497-2
- Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 1, Mathematical Surveys and Monographs, vol. 92, American Mathematical Society, Providence, RI, 2002. Hardy, Hankel, and Toeplitz; Translated from the French by Andreas Hartmann. MR 1864396
- Richard Rochberg, Toeplitz and Hankel operators on the Paley-Wiener space, Integral Equations Operator Theory 10 (1987), no. 2, 187â235. MR 878246, DOI 10.1007/BF01199078
Bibliographic Information
- Marcus Carlsson
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- Received by editor(s): February 10, 2010
- Received by editor(s) in revised form: May 20, 2010
- Published electronically: November 5, 2010
- Communicated by: Michael T. Lacey
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 1717-1733
- MSC (2010): Primary 47G10; Secondary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-2010-10598-1
- MathSciNet review: 2763760