scholarly journals The domino problem on groups of polynomial growth

2018 ◽  
Vol 12 (1) ◽  
pp. 93-105
Author(s):  
Alexis Ballier ◽  
Maya Stein
Keyword(s):  
Polynomial Growth ◽  
Groups Of Polynomial Growth

scholarly journals Besov algebras on Lie groups of polynomial growth

2012 ◽  
Vol 212 (2) ◽  
pp. 119-139 ◽  
Author(s):  
Isabelle Gallagher ◽  
Yannick Sire
Keyword(s):  
Lie Groups ◽  
Polynomial Growth ◽  
Groups Of Polynomial Growth

scholarly journals Weighted group algebras on groups of polynomial growth

2003 ◽  
Vol 245 (4) ◽  
pp. 791-821 ◽  
Author(s):  
G. Fendler ◽  
K. Gr�chenig ◽  
M. Leinert ◽  
J. Ludwig ◽  
C. Molitor-Braun
Keyword(s):  
Polynomial Growth ◽  
Group Algebras ◽  
Groups Of Polynomial Growth

scholarly journals Riesz Transforms and Lie Groups of Polynomial Growth

1999 ◽  
Vol 162 (1) ◽  
pp. 14-51 ◽  
Author(s):  
A.F.M. ter Elst ◽  
Derek W. Robinson ◽  
Adam Sikora
Keyword(s):  
Lie Groups ◽  
Polynomial Growth ◽  
Riesz Transforms ◽  
Groups Of Polynomial Growth

scholarly journals Isoperimetric Upper Bound for the First Eigenvalue of Discrete Steklov Problems

2020 ◽  
Author(s):  
Hélène Perrin
Keyword(s):  
Upper Bound ◽  
Polynomial Growth ◽  
Upper Bounds ◽  
First Eigenvalue ◽  
Zero Eigenvalue ◽  
Finite Graphs ◽  
Metric Properties ◽  
The First Eigenvalue ◽  
Steklov Eigenvalue ◽  
Groups Of Polynomial Growth

AbstractWe study upper bounds for the first non-zero eigenvalue of the Steklov problem defined on finite graphs with boundary. For finite graphs with boundary included in a Cayley graph associated to a group of polynomial growth, we give an upper bound for the first non-zero Steklov eigenvalue depending on the number of vertices of the graph and of its boundary. As a corollary, if the graph with boundary also satisfies a discrete isoperimetric inequality, we show that the first non-zero Steklov eigenvalue tends to zero as the number of vertices of the graph tends to infinity. This extends recent results of Han and Hua, who obtained a similar result in the case of $$\mathbb {Z}^n$$ Z n . We obtain the result using metric properties of Cayley graphs associated to groups of polynomial growth.

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