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.References
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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