Unitary Representations of Some Linear Groups

Author:

Itô Seizô

Abstract

Recently I. Gelfand and M. Neumark [2] have determined the types of irreducible unitary representations of the group G1 of linear transformations of the straight line. The analogous result is obtained for the group G2 of transformations zaz + b in the complex-number plane , where a and b run over all complex numbers with the exception of a = 0, which may be considered as the group of all sense-preserving similar transformations in the two-dimensional euclidean space E2.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. Stochastic processes with an integral-valued parameter;Doob;Trans. Amer. Math, Soc.,1938

2. Unitary representations of the group of linear transformations of the straight line;Gelfand;C. R. (Doklady) Acad. Sci. URSS,1947

3. Sur les fonctions aléatoires presque périodiques et sur la décomposition des fonctions aléatoires stationaires en composantes;Slutsky;Act. Sci. Ind.,1938

4. Linear Transformations in Hilbert Space and Their Applications to Analysis

5. Les fonctions de type positif et la théorie des groupes;Godement;Trans. Amer. Math. Soc.,1948

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Origins of Infinite Dimensional Unitary Representations of Lie Groups;The Intersection of History and Mathematics;1994

2. Bibliography;North-Holland Mathematical Library;1990

3. Two-Dimensional Euclidean Group and the Partial-Wave Expansion. I;Progress of Theoretical Physics;1968-05-01

4. Fundamental solutions of parabolic differential equations and boundary value problems;Japanese journal of mathematics :transactions and abstracts;1957

5. Unitary Representations of Some Linear Groups II;Nagoya Mathematical Journal;1953-02

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