One-parameter groups of isometries on Hardy spaces of the torus
Authors:
Earl Berkson and Horacio Porta
Journal:
Trans. Amer. Math. Soc. 220 (1976), 373-391
MSC:
Primary 47D10; Secondary 46J15
DOI:
https://doi.org/10.1090/S0002-9947-1976-0417855-8
MathSciNet review:
0417855
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Abstract | References | Similar Articles | Additional Information
Abstract: The strongly continuous one-parameter groups of isometries on of the torus
, as well as their generators, are classified and concretely described.
- [1]
E. Berkson, R. Kaufman and H. Porta, Möbius transformations of the disc and one-parameter groups of isometries of
, Trans. Amer. Math. Soc. 199 (1974), 223-239. MR 0361923 (50:14365)
- [2] E. Berkson and H. Porta, Hermitian operators and one-parameter groups of isometries in Hardy spaces, Trans. Amer. Math. Soc. 185 (1973), 331-344. MR 49 #3597. MR 0338833 (49:3597)
- [3] J. L. Doob, Stochastic processes, Wiley, New York; Chapman & Hall, London 1953. MR 15, 445. MR 0058896 (15:445b)
- [4] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
- [5]
N. Lal and S. Merrill, Isometries of
spaces of the torus, Proc. Amer. Math. Soc. 31 (1972), 465-471. MR 45 #5735. MR 0296676 (45:5735)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1976-0417855-8
Keywords:
Isometry,
Hardy space,
torus,
Möbius transformation,
group,
generator
Article copyright:
© Copyright 1976
American Mathematical Society