Criteria for two spectral problems of 1D operators. (Chinese. English summary) Zbl 1485.47007
Summary: This paper introduces shortly recent progress on the following three problems: the principal eigen-value in four cases, isospectral operators, and discrete spectrum, for birth-death processes and one-dimensional diffusion processes. Unified basic estimates of principal eigenvalues in various situations are obtained, the ratio of their upper and lower bounds is no more than 4. Short criteria for discrete spectrum are presented in dimension one.
MSC:
47A10 | Spectrum, resolvent |
34L05 | General spectral theory of ordinary differential operators |
60J60 | Diffusion processes |
60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |