Linear fractional transformations of Stieltjes functions
نویسندگان
چکیده
منابع مشابه
A Theory of Linear Fractional Transformations of Rational Functions
If g, g are complex rational functions, we say that g ∼ g if g = ( ax+b cx+d )−1 ◦ g ◦ (ax+b cx+d ) , where ∣∣∣∣ a b c d ∣∣∣∣ 6= 0. For practical purposes, the general problem of finding a collection of rational invariants that are sufficient to partition ∼ into equivalency classes may be intractable for arbitrary degree rational functions. In this paper, we first outline a simple and naive met...
متن کاملContractivity of linear fractional transformations
One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence...
متن کاملOrphans in Forests of Linear Fractional Transformations
A positive linear fractional transformation (PLFT) is a function of the form f(z) = az+b cz+d where a, b, c and d are nonnegative integers with determinant ad− bc 6= 0. Nathanson generalized the notion of the Calkin-Wilf tree to PLFTs and used it to partition the set of PLFTs into an infinite forest of rooted trees. The roots of these PLFT Calkin-Wilf trees are called orphans. In this paper, we...
متن کاملDifferential Subordinations for Fractional- Linear Transformations
We establish that the differential subordinations of the forms p(z)+γzp′(z)≺ h(A1,B1;z) or p(z)+γzp′(z)/p(z) ≺ h(A2,B2;z) implies p(z) ≺ h(A,B;z), where γ ≥ 0 and h(A,B;z)= (1+Az)/(1+Bz) with −1≤ B <A.
متن کاملOn Linear Fractional Transformations Associated with Generalized J-inner Matrix Functions
A class Uκ1(J) of generalized J-inner mvf’s (matrix valued functions) W (λ) which appear as resolvent matrices for bitangential interpolation problems in the generalized Schur class of p × q mvf’s S κ and some associated reproducing kernel Pontryagin spaces are studied. These spaces are used to describe the range of the linear fractional transformation TW based on W and applied to S p×q κ2 . Fa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: PAMM
سال: 2011
ISSN: 1617-7061
DOI: 10.1002/pamm.201110430