Recurrence relations for multilevel interpolations

Many remarkable properties and applications of Hermite-Padé interpolations are well known. Recently, this construction has been developed and the so-called multilevel interpolations have been introduced. Studies of their properties were motivated by applications in integrable systems (Degasperis–Procesi equation) and random matrices (two-matrix model). In addition, an important property of the perfectness of Nikishin systems for these interpolations was discovered. The talk is devoted to further properties of these interpolations. We discuss the existence of nearest neighbor recurrence relations, explicit integral formulas for the coefficients, and their boundedness. These results can be used to study the spectral properties of Jacobi matrices on trees.