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cannot be written in terms of irreducible representations, even though it is unitary and completely reducible. An example where this happens is the infinite symmetric group, where the von
Neumann group algebra is the hyperfinite type
184:, the only issue therefore being its normalization.) For general locally compact groups, or even countable discrete groups, the von Neumann group algebra need not be of type I and the regular representation of
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242:"Noncommutative harmonic analysis: in honor of Jacques Carmona", Jacques Carmona, Patrick Delorme, Michèle Vergne; Publisher Springer, 2004
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factor. The further theory divides up the
Plancherel measure into a discrete and a continuous part. For
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256:. Translated from the 1985 Russian-language edition (Kharkov, Ukraine). Birkhäuser Verlag. 1988.
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that is locally compact, not compact and not commutative. The interesting examples include many
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is abstractly given by identifying a measure on the unitary dual, the
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of irreducible representations. It is parametrized therefore by the
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is usually taken to be the extension of the theory to all groups
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Application of
Fourier analysis to non-abelian topological groups
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Noncommutaive
Harmonic Analysis: In Honor of Jacques Carmona
113:. These examples are of interest and frequently applied in
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from the 1920s, as being generally analogous to that of
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What to expect is known as the result of basic work of
276:"On the evolution of noncommutative harmonic analysis"
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82:is understood, qualitatively and after the
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97:The main task is therefore the case of
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38:is the field in which results from
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322:. American Mathematical Society.
18:Non-commutative harmonic analysis
319:Noncommutative Harmonic Analysis
36:noncommutative harmonic analysis
54:have a well-understood theory,
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226:Discrete series representation
52:locally compact abelian groups
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1:
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123:automorphic representations
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274:Gross, Kenneth I. (1978).
134:von Neumann group algebra
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231:Zonal spherical function
132:. He showed that if the
168:. The analogue of the
150:unitary representation
221:Kirillov orbit theory
211:Selberg trace formula
166:hull-kernel topology
115:mathematical physics
280:Amer. Math. Monthly
199:solvable Lie groups
140:is of type I, then
117:, and contemporary
363:Topological groups
314:Taylor, Michael E.
252:Yurii I. Lyubich.
174:Plancherel measure
170:Plancherel theorem
84:Peter–Weyl theorem
64:Fourier transforms
56:Pontryagin duality
44:topological groups
368:Harmonic analysis
216:Langlands program
197:, and classes of
195:semisimple groups
68:harmonic analysis
16:(Redirected from
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373:Duality theories
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105:, and also
48:commutative
32:mathematics
357:Categories
237:References
178:dual group
103:Lie groups
90:and their
74:that are
205:See also
50:. Since
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296:JSTOR
261:Notes
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324:ISBN
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