Pluriharmonic maps into outer symmetric spaces and a subdivision of Weyl chambers

2010 ◽  
Vol 42 (6) ◽  
pp. 1121-1133 ◽  
Author(s):  
J.-H. Eschenburg ◽  
A.-L. Mare ◽  
P. Quast
Keyword(s):  
Symmetric Spaces ◽  
Pluriharmonic Maps

scholarly journals Pluriharmonic maps into Kähler symmetric spaces and Sym’s formula

2009 ◽  
Vol 264 (2) ◽  
pp. 483-484
Author(s):  
J.-H. Eschenburg ◽  
P. Quast
Keyword(s):  
Symmetric Spaces ◽  
Pluriharmonic Maps

Pluriharmonic maps into Kähler symmetric spaces and Sym’s formula

2009 ◽  
Vol 264 (2) ◽  
pp. 469-481 ◽  
Author(s):  
J.-H. Eschenburg ◽  
P. Quast
Keyword(s):  
Symmetric Spaces ◽  
Pluriharmonic Maps

Mean ergodic theorem in function symmetric spaces for infinite measure

2018 ◽  
Vol 2018 (1) ◽  
pp. 35-46
Author(s):  
Vladimir Chilin ◽  
◽  
Aleksandr Veksler ◽  
Keyword(s):  
Ergodic Theorem ◽  
Symmetric Spaces ◽  
Infinite Measure ◽  
Mean Ergodic Theorem

scholarly journals THE SMOOTHNESS OF ORBITAL MEASURES ON NONCOMPACT SYMMETRIC SPACES

2021 ◽  
pp. 1-20
Author(s):  
SANJIV KUMAR GUPTA ◽  
KATHRYN E. HARE
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Continuous Measure ◽  
Convolution Product ◽  
Absolutely Continuous ◽  
Regular Elements ◽  
Connected Subgroup ◽  
Decay Properties ◽  
Absolutely Continuous Measure ◽  
Special Case

Abstract Let $G/K$ be an irreducible symmetric space, where G is a noncompact, connected Lie group and K is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$ continuous orbital measures has its density function in $L^{2}(G)$ and hence is an absolutely continuous measure with respect to the Haar measure. The number r is approximately the rank of $G/K$ . For the special case of the orbital measures, $\nu _{a_{i}}$ , supported on the double cosets $Ka_{i}K$ , where $a_{i}$ belongs to the dense set of regular elements, we prove the sharp result that $\nu _{a_{1}}\ast \nu _{a_{2}}\in L^{2},$ except for the symmetric space of Cartan class $AI$ when the convolution of three orbital measures is needed (even though $\nu _{a_{1}}\ast \nu _{a_{2}}$ is absolutely continuous).

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