$$H^{\varvec{\infty }}$$H∞ Interpolation and Embedding Theorems for Rational Functions
Sign Up to like & getrecommendations! Published in 2019 at "Integral Equations and Operator Theory"
DOI: 10.1007/s00020-019-2514-6
Abstract: We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc $$\mathbb {D}$$D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another application of… read more here.
Keywords: infty interpolation; varvec infty; theorems rational; embedding theorems ... See more keywords
Conjugation of Rational Functions to Power Functions and Applications to Iteration
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DOI: 10.1007/s00025-018-0801-1
Abstract: In this paper we investigate normalization of rational functions, reducing in the sense of conjugation to monomials or more general power functions. We give conditions for the normalization by computing minimal irreducible decomposition of algebraic… read more here.
Keywords: power functions; functions power; rational functions; functions applications ... See more keywords
Representation of conformal maps by rational functions
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DOI: 10.1007/s00211-019-01023-z
Abstract: The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler,… read more here.
Keywords: rational functions; representation conformal; conformal maps; maps rational ... See more keywords
Time Data-Based Iterative Method for Frequency-Domain Multivariable Systems Identification by Optimized Expansion of Rational Functions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Control, Automation and Electrical Systems"
DOI: 10.1007/s40313-019-00475-w
Abstract: This paper proposes a deterministic iterative method to obtain a linear time-invariant model of a multivariable plant from time-domain measured data. Model identification is based on frequency response matrices computed from time input–output signals which… read more here.
Keywords: iterative method; optimized expansion; rational functions; frequency ... See more keywords
Semiconjugate Rational Functions: A Dynamical Approach
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DOI: 10.1007/s40598-018-0081-6
Abstract: Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that $$A\circ X=X\circ B$$A∘X=X∘B and $${\mathbb C}(B,X)={\mathbb… read more here.
Keywords: rational functions; functions dynamical; semiconjugate rational; dynamical approach ... See more keywords
Rational functions with small value set
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DOI: 10.1016/j.jalgebra.2020.08.039
Abstract: Abstract Let q be a prime power, and let F q be the finite field with q elements. In connection with Galois theory and algebraic curves, this paper investigates rational functions h ( x )… read more here.
Keywords: value set; value; rational functions; functions small ... See more keywords
Some applications of Dubinin's lemma to rational functions with prescribed poles
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.01.069
Abstract: Abstract By developing a new technique some results for the rational functions with prescribed poles and restricted zeros have been obtained. The estimated results strengthen many well known inequalities concerning the derivative and polar derivative… read more here.
Keywords: rational functions; lemma rational; prescribed poles; dubinin lemma ... See more keywords
A refinement for rational functions of Pólya's method to construct Voronoi diagrams
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.02.071
Abstract: Abstract Given a complex polynomial P with zeroes z 1 , … , z d , we show that the asymptotic zero-counting measure of the iterated derivatives Q ( n ) , n = 1… read more here.
Keywords: voronoi diagrams; rational functions; refinement rational; functions lya ... See more keywords
Plurisubharmonic noncommutative rational functions
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DOI: 10.1016/j.jmaa.2020.124421
Abstract: Abstract A noncommutative (nc) function in x 1 , … , x g , x 1 ⁎ , … , x g ⁎ is called plurisubharmonic (plush) if its nc complex Hessian takes only positive… read more here.
Keywords: plush; noncommutative rational; rational function; plurisubharmonic noncommutative ... See more keywords
Rational functions of degree four that permute the projective line over a finite field
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DOI: 10.1080/00927872.2021.1906887
Abstract: Abstract Recently, rational functions of degree three that permute the projective line over a finite field were determined by Ferraguti and Micheli. In the present paper, using a different method, we determine all rational functions… read more here.
Keywords: projective line; line finite; rational functions; functions degree ... See more keywords
Heun functions and diagonals of rational functions
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ab67e5
Abstract: We provide a set of diagonals of simple rational functions of three and four variables that are squares of Heun functions. These Heun functions obtained through creative telescoping, turn out to be either pullbacked $_2F_1$… read more here.
Keywords: functions diagonals; rational functions; heun functions; functions heun ... See more keywords