×
Farashahi, Arash Ghaani

Abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups. (English) Zbl 1360.43006

J. Aust. Math. Soc. 101, No. 2, 171-187 (2016).
Summary: This paper presents a structured study for abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups. Let \(H,K\) be locally compact groups and \(\theta:H\to\mathrm{Aut}(K)\) be a continuous homomorphism. Let \(G_\theta=H\ltimes_\theta K\) be the semidirect product of \(H\) and \(K\) with respect to \(\theta\) and \(G_\theta/H\) be the canonical homogeneous space (left coset space) of \(G_\theta/H\). We present a unified approach to the harmonic analysis of relative convolutions over the canonical homogeneous space \(G_\theta/H\).

Cited in 9 Documents

MSC:

43A85 Harmonic analysis on homogeneous spaces
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.

Keywords:

canonical homogeneous space of semidirect groups; rho-function; \(\theta\)-convolution; \(\theta\)-involution; relative convolutions
Cite Review PDF
Full Text: DOI

References:

[1] Reiter, Classical Harmonic Analysis (2000) · Zbl 0965.43001
[2] DOI: 10.1007/s13324-013-0057-6 · Zbl 1321.43003 · doi:10.1007/s13324-013-0057-6
[3] Kisil, Eurasian Math. J. 5 pp 95– (2014)
[4] DOI: 10.1007/s40840-014-0049-1 · Zbl 1311.43007 · doi:10.1007/s40840-014-0049-1
[5] DOI: 10.1142/p835 · Zbl 1254.30001 · doi:10.1142/p835
[6] DOI: 10.1007/s00025-014-0407-1 · Zbl 1315.43004 · doi:10.1007/s00025-014-0407-1
[7] DOI: 10.1006/aima.1999.1833 · Zbl 0933.43004 · doi:10.1006/aima.1999.1833
[8] DOI: 10.1007/s13324-013-0065-6 · Zbl 1312.43002 · doi:10.1007/s13324-013-0065-6
[9] DOI: 10.1007/BF01378780 · Zbl 0840.43020 · doi:10.1007/BF01378780
[10] Ghaani Farashahi, Bull. Malays. Math. Sci. Soc. (2) 36 pp 1109– (2013)
[11] Hochschild, The Structure of Lie Groups (1965) · Zbl 0131.02702
[12] Hewitt, Abstract Harmonic Analysis, Vol. 2 (1970) · Zbl 0213.40103
[13] Folland, A Course in Abstract Harmonic Analysis (1995)
[14] Hewitt, Abstract Harmonic Analysis, Vol. 1 (1963) · Zbl 0115.10603
[15] Chirikjian, Engineering Applications of Noncommutative Harmonic Analysis with Emphasis on Rotation and Motion Groups (2001) · Zbl 1100.42500
[16] Ghaani Farashahi, Southeast Asian Bull. Math. 40 pp 1– (2016)
[17] DOI: 10.1007/s12220-009-9069-8 · Zbl 1168.43002 · doi:10.1007/s12220-009-9069-8
[18] DOI: 10.1142/S021969130800263X · Zbl 1151.81342 · doi:10.1142/S021969130800263X
[19] DOI: 10.15352/bjma/1396640061 · Zbl 1305.43009 · doi:10.15352/bjma/1396640061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.