Representation of functions by matrices. Application to Faber polynomials

Faber Polynomials for Rational Mapping Functions

Faber Polynomials of Matrices for Non-convex Sets

It has been recently shown that ||Fn(A)|| ≤ 2, where A is a linear continuous operator acting in a Hilbert space, and Fn is the Faber polynomial of degree n corresponding to some convex compact E ⊂ C containing the numerical range of A. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods. In the present paper we ext...

Faber Polynomials Corresponding to Rational Exterior Mapping Functions

Faber polynomials corresponding to rational exterior mapping functions of degree (m,m − 1) are studied. It is shown that these polynomials always satisfy an (m + 1)-term recurrence. For the special case m = 2, it is shown that the Faber polynomials can be expressed in terms of the classical Chebyshev polynomials of the first kind. In this case, explicit formulas for the Faber polynomials are de...

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Lattice Paths and Faber Polynomials

The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.