The ordinary and matrix continued fractions in the theoretical analysis of Hermitian and relaxation operators (Q1119842)

The paper is concerned with decompositions of the operator form \((I- H)^{-1}\), where I is a unit operator and the operator H is prescribed. With P(0), P(1) projection operators and \(H(\tau,\nu)=P(\tau)HP(\nu)\) \((\tau,\nu =0,1)\), \(P(O)(I-H)^{-1}(P(0)\) is expressed as \(\{I-H(0,0)- H(0,1)\{I-H(1,1)\}^{-1}H(1,0)\}^{-1}\). This decomposition is iterated to obtain a continued fraction. Applications of the theory of physics are considered.