scholarly journals $L^p-L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

2001 ◽  
Vol 51 (4) ◽  
pp. 1047-1069 ◽  
Author(s):  
Michael Cowling ◽  
Saverio Giulini ◽  
Stefano Meda
Keyword(s):  
Symmetric Spaces ◽  
Beltrami Operator

$L^p - L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I

1993 ◽  
Vol 72 (1) ◽  
pp. 109-150 ◽  
Author(s):  
Michael Cowling ◽  
Saverio Giulini ◽  
Stefano Meda
Keyword(s):  
Symmetric Spaces ◽  
Beltrami Operator

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 Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

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