An homotopy of isometries related to a probability density
  We are studying here a family of probability density functions indexed by a real parameter, and constructed from homographic relations between associated Stieltjes transforms. From the analysis of orthogonal polynomials we deduce a family of isometries in relation to the classical operators creating secondary polynomials and we give an application to the explicit resolution of specific integral equations. 
Roland Groux
math.CA