Abstract
In this paper, we prove a variational formula for Dirichlet forms generated by general symmetric Markov processes. As its applications, we obtain lower bound estimates of the bottom of spectrum for symmetric Markov processes. Moreover, for a positive measure μ charging no set of zero capacity, we give a new proof of an L 2(μ)-estimate of functions in Dirichlet spaces. Finally, we calculate the principal eigenvalues for absorbing and time changed α-stable processes and obtain conditions for some measures being gaugeable.
| Original language | English |
|---|---|
| Pages (from-to) | 135-151 |
| Number of pages | 17 |
| Journal | Potential Analysis |
| Volume | 23 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Sep 1 2005 |
Keywords
- Dirichlet form
- Principal eigenvalue
- Symmetric α-stable process
- Time change
- Variational formula
ASJC Scopus subject areas
- Analysis
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Shiozawa, Y., & Takeda, M. (2005). Variational formula for dirichlet forms and estimates of principal eigenvalues for symmetric α-stable processes. Potential Analysis, 23(2), 135-151. https://doi.org/10.1007/s11118-004-5392-7