One-parameter groups of isometries on Hardy spaces of the torus: spectral theory

Berkson, Earl; Porta, Horacio

doi:10.1090/S0002-9947-1977-0451035-6

One-parameter groups of isometries on Hardy spaces of the torus: spectral theory
HTML articles powered by AMS MathViewer

by Earl Berkson and Horacio Porta

Trans. Amer. Math. Soc. 227 (1977), 357-370

DOI: https://doi.org/10.1090/S0002-9947-1977-0451035-6

PDF | Request permission

Abstract:

The spectral theory of the infinitesimal generator of an arbitrary one-parameter group of isometries on ${H^p}$ of the torus, $1 \leqslant p < \infty ,p \ne 2$, is considered. In particular, the spectrum of the generator is determined.

References

Earl Berkson, Robert Kaufman, and Horacio Porta, Möbius transformations of the disc and one-parameter groups of isometries of $H^{p}$, Trans. Amer. Math. Soc. 199 (1974), 223–239. MR 361923, DOI 10.1090/S0002-9947-1974-0361923-4
Earl Berkson and Horacio Porta, Hermitian operators and one-parameter groups of isometries in Hardy spaces, Trans. Amer. Math. Soc. 185 (1973), 331–344 (1974). MR 338833, DOI 10.1090/S0002-9947-1973-0338833-0
Earl Berkson and Horacio Porta, One-parameter groups of isometries on Hardy spaces of the torus, Trans. Amer. Math. Soc. 220 (1976), 373–391. MR 417855, DOI 10.1090/S0002-9947-1976-0417855-8
Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
Nand Lal and Samuel Merrill III, Isometries of $H^{p}$ spaces of the torus, Proc. Amer. Math. Soc. 31 (1972), 465–471. MR 296676, DOI 10.1090/S0002-9939-1972-0296676-5
Samuel Merrill III and Nand Lal, Characterization of certain invariant subspaces of $H^{p}$ and $L^{p}$ spaces derived from logmodular algebras, Pacific J. Math. 30 (1969), 463–474. MR 248526, DOI 10.2140/pjm.1969.30.463