We study nonsymmetric tridiagonal operators acting in the Hilbert space l and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a connection between Padé approximants and spectral properties of nonsymmetric tridiagonal operators.

In order to calculate the energy when 0127 is small, we expand the right-hand side of the BrillouinWigner equation in terms of a coupling constant 03BB. Both hierarchies in 0127 and 03BB are connected. The Padé approximants of the right-hand side converge. Tome 40 N° 2 15 JANVIER 1979 LE JOURNAL DE PHYSIQUE LETTRES

While the concept of Padé approximant is essentially several centuries old, its multivariate version dates only from the early seventies. In the last century many univariate convergence results were proven, describing the approximation power for several function classes. It is not our aim to give a general review of the univariate case, but to discuss only these theorems that have a multivariat...

The response function for a general class of elastic molecular based materials characterized by their limiting molecular chain extensibility and depending on only the first principal invariant of the Cauchy–Green deformation tensor together with a certain molecular based limiting extensibility parameter is introduced. The constitutive response function for the Gent material is then derived inve...