scholarly journals The Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces—the local theory

2005 ◽  
Vol 220 (1) ◽  
pp. 97-117 ◽  
Author(s):  
Roberto Camporesi
Keyword(s):  
Fourier Transform ◽  
Symmetric Spaces ◽  
Vector Bundles ◽  
Local Theory ◽  
Riemannian Symmetric Spaces ◽  
Homogeneous Vector

scholarly journals Characterization of Dini Lipschitz Functions in Terms of Their Helgason Transform

2016 ◽  
Vol 54 (2) ◽  
pp. 117-130
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Fourier Transform ◽  
Lipschitz Condition ◽  
Symmetric Spaces ◽  
Translation Operator ◽  
Lipschitz Functions ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Rank One ◽  
Riemannian Symmetric Spaces

Abstract In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [6] for the Helgason Fourier transform of a set of functions satisfying the Dini Lipschitz condition in the space L2 for functions on noncompact rank one Riemannian symmetric spaces.

scholarly journals HEAT KERNEL ON HOMOGENEOUS BUNDLES

2008 ◽  
Vol 05 (03) ◽  
pp. 407-429 ◽  
Author(s):  
IVAN G. AVRAMIDI
Keyword(s):  
Integral Representation ◽  
Heat Kernel ◽  
Generating Function ◽  
Symmetric Spaces ◽  
Vector Bundles ◽  
Formal Solution ◽  
Analytical Continuation ◽  
Semi Group ◽  
Heat Invariants ◽  
Homogeneous Vector

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization and analytical continuation.

scholarly journals Fano 3-folds from homogeneous vector bundles over Grassmannians

2021 ◽  
Author(s):  
Lorenzo De Biase ◽  
Enrico Fatighenti ◽  
Fabio Tanturri
Keyword(s):  
Vector Bundles ◽  
Homogeneous Vector

AbstractWe rework the Mori–Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.

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