Results 121 to 130 of about 186 (152)

ON THE LOCATION OF THE ZEROS OF FABER POLYNOMIALS

Analysis, 2000
Let \(\Omega\) denote a compact set in \(\overline\mathbb{C}\), \(\Omega \neq\{a\}\) and such that \(\overline\mathbb{C}\setminus\Omega\) is a simply connected domain. Suppose that \(F_n(z)\) denotes the \(n\)-th Faber polynomial for \(\Omega\). It is known that if \(\Omega\) is a convex set, \(int(G)\neq \emptyset\), then all the zeros of \(F_n(z ...
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The Faber polynomials for circular lunes

Computers and Mathematics With Applications, 1995
Let \(D_\alpha\) be the circular lune symmetric with respect to both axis with vertices at \(z = \pm \alpha\) and exterior angle \(\alpha \pi\), \(0 < \alpha \leq 2\). Let \(z = \psi (w) = w + \sum^\infty_{k = 0} b_k w^{-k}\) map \(\{w : |w |> 1\}\) conformally onto the exterior of \(D_\alpha\).
exaly   +4 more sources

FUNDAMENTAL PROPERTIES OF FABER POLYNOMIALS

Russian Mathematical Surveys, 1964
CONTENTSIntroduction § 1. Estimates for Faber polynomials within the domain § 2. Asymptotic formulae § 3. Convergence of Faber series within the domain § 4. Convergence of Faber series in the closed domain § 5. Series of Faber polynomials § 6. On the uniqueness of series of Faber polynomials § 7. Application of Faber polynomials to the interpolation of
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Faber Polynomials on Quaternionic Compact Sets

Complex Analysis and Operator Theory, 2017
The authors consider the notion of Faber polynomials in the context of slice regular quaternionic functions. Let \(K\) be an axially symmetric compact set in \(\mathbb H\) (the skew field of real quaternions) such that \(\overline{\mathbb H}\setminus K\) is simply connected, then a given quaternionic function which is continuous on \(K\) and slice ...
Gal, Sorin G., Sabadini, Irene
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Exact estimates for Faber polynomials and for norm of Faber operator

Complex Variables and Elliptic Equations, 2019
Exact estimates for Faber polynomials, norm of Faber operator, and L1-norm of the generating function for the sequence of Faber operator of univalent functions of class Σ are found.
F. G. Abdullayev, V. V. Savchuk, T. Tunç   +2 more
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The conformal ‘bratwurst’ mapsand associated Faber polynomials

Numerische Mathematik, 2000
In the construction of polynomial iteration methods for the solution of a linear system \(Ax= b\), it is necessary to find inclusion sets \(\Omega\) which contain the spectrum of \(A\) but \(0\not\in\Omega\). The main object of this paper is to construct explicitly a class of non-convex inclusion sets.
Tino Koch, Jörg Liesen
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Lattice Paths and Faber Polynomials

1997
The r-th Faber polynomial of the Laurent series f(t) = t + f 0 + f 1/t + f 2/t 2 + … is the unique polynomial F r (u) of degree r in u such that F r (f) = t r + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.
Ira M. Gessel, Sangwook Ree
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Application of Faber Polynomials in Proving Combinatorial Identities

Ukrainian Mathematical Journal, 2018
Suppose \(K\) is a compact subset of \(\mathbb C\) containing at least \(2\) points. If the complement of \(K\) in the Riemann sphere \(\overline{\mathbb C}=\mathbb C\cup\{\infty\}\) is simply connected, then the Riemann mapping theorem guarantees that there exists a unique biholomorphic map \(\Phi:\overline{\mathbb C}\setminus K\to\{w\in\overline ...
Abdullaev, F. G., Imash-kyzy, M., Savchuk, V. V.   +2 more
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Studies In Faber Polynomials.

1962
PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/185361/2/6202692 ...
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Supplement to Explicit Faber Polynomials on Circular Sectors

Mathematics of Computation, 1992
This is an appendix to the paper reviewed above. There it is shown how the coefficients of the Faber polynomials on circular sectors \(S_ \alpha\) can be represented in terms of polynomials in \(c:=\alpha(2\pi- \alpha)/\pi\). For Faber polynomials up to degree 20 all the corresponding polynomials in \(c\) are given.
Gatermann, Karin, Hoffmann, Christoph, Opfer, Gerhard   +2 more
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