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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Wiener-Hopf operators on a finite interval and Schatten-von Neumann classes
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by Vladimir V. Peller PDF
Proc. Amer. Math. Soc. 104 (1988), 479-486 Request permission

Abstract:

Recently R. Rochberg has characterized Hankel and Toeplitz operators on the Paley-Wiener space which belong to the Schatten-von Neumann class ${S_p}$ for $p \geq 1$. These operators coincide up to Fourier transform with Wiener-Hopf operators on a finite interval. Using a different approach, we extend Rochberg’s result to all positive $p$.
References
  • I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142
  • Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142, DOI 10.1090/coll/019
  • Jaak Peetre, New thoughts on Besov spaces, Duke University Mathematics Series, No. 1, Duke University, Mathematics Department, Durham, N.C., 1976. MR 0461123
  • V. V. Peller, Hankel operators of class ${\mathfrak {S}}_{p}$ and their applications (rational approximation, Gaussian processes, the problem of majorization of operators), Mat. Sb. (N.S.) 113(155) (1980), no. 4(12), 538–581, 637 (Russian). MR 602274
  • V. V. Peller, Description of Hankel operators of the class ${\mathfrak {S}}_{p}$ for $p>0$, investigation of the rate of rational approximation and other applications, Mat. Sb. (N.S.) 122(164) (1983), no. 4, 481–510 (Russian). MR 725454
  • Richard Rochberg, Toeplitz and Hankel operators on the Paley-Wiener space, Integral Equations Operator Theory 10 (1987), no. 2, 187–235. MR 878246, DOI 10.1007/BF01199078
  • S. Ju. Rotfel′d, Remarks on the singular values of a sum of completely continuous operators, Funkcional. Anal. i Priložen 1 (1967), no. 3, 95–96 (Russian). MR 0220094
  • Stephen Semmes, Trace ideal criteria for Hankel operators, and applications to Besov spaces, Integral Equations Operator Theory 7 (1984), no. 2, 241–281. MR 750221, DOI 10.1007/BF01200377
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 104 (1988), 479-486
  • MSC: Primary 47B35; Secondary 47B10
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0962816-7
  • MathSciNet review: 962816