Comparison Theorems for the Spectral Gap of Diffusions Processes and Schrödinger Operators on an Interval
نویسنده
چکیده
We compare the spectral gaps and thus the exponential rates of convergence to equilibrium for ergodic one-dimensional diffusions on an interval. One of the results may be thought of as the diffusion analog of a recent result for the spectral gap of one-dimensional Schrödinger operators. We also discuss the similarities and differences between spectral gap results for diffusions and for Schrödinger operators.
منابع مشابه
Multidimensional Schrödinger Operators and Spectral Theory
Here we present some fundamental theorems of Schrödinger operators and their spectral theory.
متن کاملInverse spectral problems for Sturm-Liouville operators with transmission conditions
Abstract: This paper deals with the boundary value problem involving the differential equation -y''+q(x)y=lambda y subject to the standard boundary conditions along with the following discontinuity conditions at a point y(a+0)=a1y(a-0), y'(a+0)=a2y'(a-0)+a3y(a-0). We develop the Hochestadt-Lieberman’s result for Sturm-Lio...
متن کاملOn inverse problem for singular Sturm-Liouville operator with discontinuity conditions
In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse proble...
متن کاملInverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...
متن کاملUniqueness Theorems in Inverse Spectral Theory for One-dimensional Schrödinger Operators
New unique characterization results for the potential V (x) in connection with Schrödinger operators on R and on the half-line [0,∞) are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for Schrödinger operators on the half-line with purely discrete spectra to arbitrary sp...
متن کامل