Continuous Partial Gabor Transform for Semi-Direct Product of Locally Compact Groups

Freudenthal [5, 7] defined a compactification of a rim-compact space, that is, a space having a base of open sets with compact boundary. The additional points are called ends and Freudenthal showed that a connected locally compact non-compact group having a countable base has one or two ends. Later, Freudenthal [8], Zippin [16], and Iwasawa [11] showed that a connected locally compact group has two ends if and only if it is the direct product of a compact group and the reals.

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Qualitative uncertainty principle for the Gabor transform on certain locally compact groups

Advances in Pure and Applied Mathematics ◽

10.1515/apam-2017-0050 ◽

2018 ◽

Vol 9 (3) ◽

pp. 205-220

Author(s):

Jyoti Sharma ◽

Ajay Kumar

Keyword(s):

Lie Groups ◽

Uncertainty Principle ◽

Discrete Group ◽

Locally Compact Groups ◽

Gabor Transform ◽

Compact Groups ◽

Nilpotent Lie Groups ◽

Locally Compact ◽

Qualitative Uncertainty ◽

Low Dimensional

Abstract Several classes of locally compact groups have been shown to possess a qualitative uncertainty principle for the Gabor transform. These include Moore groups, the Heisenberg group {\mathbb{H}_{n}} , the group {\mathbb{H}_{n}\times D} (where D is a discrete group) and other low-dimensional nilpotent Lie groups.

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A Unified Group Theoretical Method for the Partial Fourier Analysis on Semi-Direct Product of Locally Compact Groups

Results in Mathematics ◽

10.1007/s00025-014-0407-1 ◽

2014 ◽

Vol 67 (1-2) ◽

pp. 235-251 ◽

Cited By ~ 4

Author(s):

Arash Ghaani Farashahi

Keyword(s):

Fourier Analysis ◽

Direct Product ◽

Theoretical Method ◽

Locally Compact Groups ◽

Compact Groups ◽

Locally Compact ◽

Group Theoretical Method

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Approximation property of C*-algebraic bundles

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004101005837 ◽

2002 ◽

Vol 132 (3) ◽

pp. 509-522 ◽

Cited By ~ 11

Author(s):

RUY EXEL ◽

CHI-KEUNG NG

Keyword(s):

Direct Product ◽

Approximation Property ◽

Discrete Case ◽

Locally Compact Groups ◽

Compact Groups ◽

Discrete Groups ◽

Locally Compact ◽

Cross Sectional ◽

The Cross

In this paper, we will define the reduced cross-sectional C*-algebras of C*-algebraic bundles over locally compact groups and show that if a C*-algebraic bundle has the approximation property (defined similarly as in the discrete case), then the full cross-sectional C*-algebra and the reduced one coincide. Moreover, if a semi-direct product bundle has the approximation property and the underlying C*-algebra is nuclear, then the cross-sectional C*-algebra is also nuclear. We will also compare the approximation property with the amenability of Anantharaman-Delaroche in the case of discrete groups.

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The reduced dual of a direct product of groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100039438 ◽

1966 ◽

Vol 62 (1) ◽

pp. 5-6 ◽

Cited By ~ 2

Author(s):

Aubrey Wulfsohn

Keyword(s):

Direct Product ◽

Locally Compact Groups ◽

Compact Groups ◽

Type I ◽

Locally Compact ◽

Product Of Groups

AbstractIf one of the locally compact groups H and K is of type I, the reduced dual of their product is shown to be homeomorphic to the product of the reduced duals.

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The left Hilbert algebra associated to a semi-direct product

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100054074 ◽

1977 ◽

Vol 82 (3) ◽

pp. 411-418 ◽

Cited By ~ 4

Author(s):

R. Rousseau

Keyword(s):

Direct Product ◽

Compact Support ◽

Continuous Functions ◽

Crossed Product ◽

Locally Compact Groups ◽

Compact Groups ◽

Hilbert Algebra ◽

Locally Compact ◽

Continuous Action ◽

Canonical Weight

AbstractLet A and G be locally compact groups and α a continuous action of G on A, and let denote the semi-direct product of A and G. Then we prove that the left Hilbert algebra of continuous functions with compact support, has the same achieved left Hilbert algebra, as the crossed product of K(A)" by the associated action α̃ of G on . As a consequence we obtain that the canonical weight on is the dual weight of the canonical weight on K(A)".

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