Stieltjes product

To show this is left as an exercise. The essential point is contained in Problem 1.2.2, which tells us that the Stieltjes product (1.2.29), in the non-aging case, is commutative, so that k(t) can be moved across the viscoelastic functions. It must be positive in the sense that [k du]>0 for all positive functions u(t), if the inequalities are to remain unaffected. 

The passage from the Stieltjes to the Cauchy integral via the Dirac-Lebesgue measure for discretization of inner products 183... 

The space structure via the scalar product as the generalized Stieltjes integral... 

These zeros uk of QK(u) coincide with the eigenvalues of both the evolution matrix U and the corresponding Hessenberg matrix H from Eqs. (131) and (130), respectively. The zeros of Qk(u) are called eigenzeros. The structure of CM is determined by its scalar product for analytic functions of complex variable z or u. For any two regular functions/(m) and g(u) from CM, the scalar product in CM is defined by the generalized Stieltjes integral ... 

The product-difference (PD) algorithm was developed by Gordon (1968) and is based on the theory of continued fractions of Stieltjes. The first step is to construct a matrix P with... 

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