h TRANSFORM OF ONE-DIMENSIONAL GENERALIZED DIFFUSION OPERATORS
Tomoko Takemura, Matsuyo Tomisaki · Kyushu Journal of Mathematics · 2012
We are concerned with two types of h transform of one-dimensional generalized diffusion operators treated by Maeno (2006) and by Tomisaki (2007). We show that these two types of h transform are in inverse relation to each other in some sense. Further, we show that a recurrent one-dimensional generalized diffusion operator cannot be represented as an h transform of another one-dimensional generalized diffusion operator different from the original one. We also consider a spectral representation of elementary solutions corresponding to h transformed one-dimensional generalized diffusion operators.