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Unitary representations of the affine group. (English) Zbl 0162.58403

Summary: The unitary representations of the affine group, or the group of linear transformations without reflections on the real line, have been found previously by Gel’fand and Naĭmark. The present paper gives an alternate proof, and presents several properties of the representations which will be used in a later application of this group to continuous representations of Hilbert space. The development follows closely that used by von Neumann to prove the uniqueness of the Schrödinger operators.

MSC:

22E99 Lie groups
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[1] DOI: 10.1063/1.1704107 · Zbl 0137.23901 · doi:10.1063/1.1704107
[2] DOI: 10.1063/1.1704107 · Zbl 0137.23901 · doi:10.1063/1.1704107
[3] Gel’fand I. M., Dokl. Akad. Nauk SSSR 55 pp 570– (1947)
[4] DOI: 10.1007/BF01457956 · Zbl 0001.24703 · doi:10.1007/BF01457956
[5] Peter F., Math. Ann. 96 pp 737– (1926)
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