Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to the Sphere

2004 ◽  
Vol 21 (1/2) ◽  
pp. 147-180 ◽  
Author(s):  
Stephan Dahlke ◽  
Gabriele Steidl ◽  
Gerd Teschke
Keyword(s):  
Homogeneous Spaces ◽  
Banach Frames ◽  
Coorbit Spaces

scholarly journals Shearlet coorbit spaces and associated Banach frames

2009 ◽  
Vol 27 (2) ◽  
pp. 195-214 ◽  
Author(s):  
Stephan Dahlke ◽  
Gitta Kutyniok ◽  
Gabriele Steidl ◽  
Gerd Teschke
Keyword(s):  
Banach Frames ◽  
Coorbit Spaces

COORBIT SPACE THEORY FOR THE TOEPLITZ SHEARLET TRANSFORM

2012 ◽  
Vol 10 (04) ◽  
pp. 1250037 ◽  
Author(s):  
STEPHAN DAHLKE ◽  
SÖREN HÄUSER ◽  
GERD TESCHKE
Keyword(s):  
Space Theory ◽  
Atomic Decompositions ◽  
Banach Frames ◽  
Shearlet Transform ◽  
Coorbit Spaces ◽  
Coorbit Space Theory ◽  
Arbitrary Space

In this paper we are concerned with the continuous shearlet transform in arbitrary space dimensions where the shear operation is of Toeplitz type. In particular, we focus on the construction of associated shearlet coorbit spaces and on atomic decompositions and Banach frames for these spaces.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

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