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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Spectral decompositions of one-parameter groups of isometries on Hardy spaces
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by Dimitri Karayannakis PDF
Trans. Amer. Math. Soc. 311 (1989), 147-166 Request permission

Abstract:

Spectral decompositions of strongly continuous one-parameter groups of surjective isometries on Hardy spaces of the disk ${\mathbf {D}}$ and the torus ${{\mathbf {T}}^2}$ are examined; a concrete description of the (pointwise) action of these decompositions is presented, mainly in the parabolic case, leading to a complete description of the action of the partial sum-operators of M. Riesz when carried from ${L^p}({\mathbf {R}})$ to ${H^p}({\mathbf {D}})$, $1 < p \leq 2$. The (pointwise) action of the spectral decompositions of these isometric groups on ${H^p}({{\mathbf {T}}^2})$, $1 < p < \infty$ is also examined and concrete descriptions are derived, mainly in the parabolic case.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 147-166
  • MSC: Primary 47D05; Secondary 30D55, 42A45, 43A50, 46E15
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0948192-X
  • MathSciNet review: 948192