On the product formula on noncompact Grassmannians

Piotr Graczyk, and Patrice Sawyer. "On the product formula on noncompact Grassmannians." Colloquium Mathematicae 133.2 (2013): 145-167. <http://eudml.org/doc/284097>.

@article{PiotrGraczyk2013,
abstract = {We study the absolute continuity of the convolution $δ_\{e^X\}^\{♮\} * δ_\{e^Y\}^\{♮\}$ of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of absolute continuity of convolution powers of an orbital measure $δ_\{e^X\}^♮$.},
author = {Piotr Graczyk, Patrice Sawyer},
journal = {Colloquium Mathematicae},
keywords = {symmetric space; product formula; orbital measure},
language = {eng},
number = {2},
pages = {145-167},
title = {On the product formula on noncompact Grassmannians},
url = {http://eudml.org/doc/284097},
volume = {133},
year = {2013},
}

TY - JOUR
AU - Piotr Graczyk
AU - Patrice Sawyer
TI - On the product formula on noncompact Grassmannians
JO - Colloquium Mathematicae
PY - 2013
VL - 133
IS - 2
SP - 145
EP - 167
AB - We study the absolute continuity of the convolution $δ_{e^X}^{♮} * δ_{e^Y}^{♮}$ of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of absolute continuity of convolution powers of an orbital measure $δ_{e^X}^♮$.
LA - eng
KW - symmetric space; product formula; orbital measure
UR - http://eudml.org/doc/284097
ER -