2003, 2003(Special): 678-687. doi: 10.3934/proc.2003.2003.678

Quasi-regular graphs, cogrowth, and amenability

1. 

Dept. of Mathematics, Plattsburgh State University, Plattsburgh, NY 12901, United States

Received  September 2002 Revised  March 2003 Published  April 2003

We extend Grigrochuk’s cogrowth criterion for amenability of groups to the case of non-regular graphs for which a certain regularity condition is satisfied. The proof involves generalized Laplacians which are inverses of growth series and whose determinants are closely related to zeta functions of graphs.
Citation: Sam Northshield. Quasi-regular graphs, cogrowth, and amenability. Conference Publications, 2003, 2003 (Special) : 678-687. doi: 10.3934/proc.2003.2003.678
[1]

Nicola Abatangelo. Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5555-5607. doi: 10.3934/dcds.2015.35.5555

[2]

Shiping Cao, Hua Qiu. Boundary value problems for harmonic functions on domains in Sierpinski gaskets. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1147-1179. doi: 10.3934/cpaa.2020054

[3]

Laura Abatangelo, Susanna Terracini. Harmonic functions in union of chambers. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5609-5629. doi: 10.3934/dcds.2015.35.5609

[4]

Soonki Hong, Seonhee Lim. Martin boundary of brownian motion on Gromov hyperbolic metric graphs. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3725-3757. doi: 10.3934/dcds.2021014

[5]

Anton Petrunin. Harmonic functions on Alexandrov spaces and their applications. Electronic Research Announcements, 2003, 9: 135-141.

[6]

Dag Lukkassen, Annette Meidell, Peter Wall. On the conjugate of periodic piecewise harmonic functions. Networks and Heterogeneous Media, 2008, 3 (3) : 633-646. doi: 10.3934/nhm.2008.3.633

[7]

Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 41-74. doi: 10.3934/dcdsb.2010.14.41

[8]

Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 75-109. doi: 10.3934/dcdsb.2010.14.75

[9]

Dan Mangoubi. A gradient estimate for harmonic functions sharing the same zeros. Electronic Research Announcements, 2014, 21: 62-71. doi: 10.3934/era.2014.21.62

[10]

Matthew B. Rudd, Heather A. Van Dyke. Median values, 1-harmonic functions, and functions of least gradient. Communications on Pure and Applied Analysis, 2013, 12 (2) : 711-719. doi: 10.3934/cpaa.2013.12.711

[11]

VicenŢiu D. RǍdulescu, Somayeh Saiedinezhad. A nonlinear eigenvalue problem with $ p(x) $-growth and generalized Robin boundary value condition. Communications on Pure and Applied Analysis, 2018, 17 (1) : 39-52. doi: 10.3934/cpaa.2018003

[12]

Shenzhou Zheng, Xueliang Zheng, Zhaosheng Feng. Optimal regularity for $A$-harmonic type equations under the natural growth. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 669-685. doi: 10.3934/dcdsb.2011.16.669

[13]

Shenzhou Zheng, Laping Zhang, Zhaosheng Feng. Everywhere regularity for P-harmonic type systems under the subcritical growth. Communications on Pure and Applied Analysis, 2008, 7 (1) : 107-117. doi: 10.3934/cpaa.2008.7.107

[14]

Seppo Granlund, Niko Marola. Phragmén--Lindelöf theorem for infinity harmonic functions. Communications on Pure and Applied Analysis, 2015, 14 (1) : 127-132. doi: 10.3934/cpaa.2015.14.127

[15]

Raf Cluckers, Julia Gordon, Immanuel Halupczok. Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups. Electronic Research Announcements, 2014, 21: 137-152. doi: 10.3934/era.2014.21.137

[16]

Gershon Kresin, Vladimir Maz’ya. Optimal estimates for the gradient of harmonic functions in the multidimensional half-space. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 425-440. doi: 10.3934/dcds.2010.28.425

[17]

Fausto Ferrari, Qing Liu, Juan Manfredi. On the characterization of $p$-harmonic functions on the Heisenberg group by mean value properties. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2779-2793. doi: 10.3934/dcds.2014.34.2779

[18]

Lizhi Zhang, Congming Li, Wenxiong Chen, Tingzhi Cheng. A Liouville theorem for $\alpha$-harmonic functions in $\mathbb{R}^n_+$. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1721-1736. doi: 10.3934/dcds.2016.36.1721

[19]

Dorina Mitrea and Marius Mitrea. Boundary integral methods for harmonic differential forms in Lipschitz domains. Electronic Research Announcements, 1996, 2: 92-97.

[20]

Palle Jorgensen, James Tian. Harmonic analysis of network systems via kernels and their boundary realizations. Discrete and Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021105

 Impact Factor: 

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]