Back to Search
Start Over
Sobolev-type inequalities and eigenvalue growth on graphs with finite measure.
- Source :
-
Proceedings of the American Mathematical Society . Aug2023, Vol. 151 Issue 8, p3401-3414. 14p. - Publication Year :
- 2023
-
Abstract
- In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*DIRICHLET forms
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 163842781
- Full Text :
- https://doi.org/10.1090/proc/14361