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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. [Pg.81]

The passage from the Stieltjes to the Cauchy integral via the Dirac-Lebesgue measure for discretization of inner products 183... [Pg.145]

The space structure via the scalar product as the generalized Stieltjes integral... [Pg.183]

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 ... [Pg.183]

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... [Pg.51]


See other pages where Stieltjes product is mentioned: [Pg.5]    [Pg.81]    [Pg.5]    [Pg.81]   
See also in sourсe #XX -- [ Pg.5 , Pg.38 , Pg.43 , Pg.50 ]




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Stieltjes

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