TAUBERIAN THEOREM FOR HARMONIC MEAN OF STIELTJES TRANSFORMS AND ITS APPLICATIONS TO LINEAR DIFFUSIONS
Yuji Kasahara, Shinichi Kotani · Institutional Repositories DataBase (IRDB) · 2016
When two Radon measures on the half line are given, the harmonic mean of their Stieltjes transforms is again the Stieltjes transform of a Radon measure. We study the relationship between the asymptotic behavior of the resulting measure and those of the original ones. The problem comes from the spectral theory of second--order differential operators and the results are applied to linear diffusions neither boundaries of which is regular.