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Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.

Pietro Poggi-Corradini (2003)

Revista Matemática Iberoamericana

A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk D. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880's to the 1980's, have provided conjugations which yield very precise descriptions of the dynamics. Backward-iteration sequences are of a different nature because a point could have infinitely many preimages as well as none. However, if we insist in choosing preimages that are at a...

Baker domains for Newton’s method

Walter Bergweiler, David Drasin, James K. Langley (2007)

Annales de l’institut Fourier

For an entire function f let N ( z ) = z - f ( z ) / f ′ ( z ) be the Newton function associated to f . Each zero ξ of f is an attractive fixed point of N and is contained in an invariant component of the Fatou set of the meromorphic function N in which the iterates of N converge to ξ . If f has an asymptotic representation f ( z ) ∼ exp ( - z n ) , n ∈ ℕ , in a sector | arg z | < ε , then there exists an invariant component of the Fatou set where the iterates of N tend to infinity. Such a component is called an invariant Baker domain.A question in the opposite direction...

Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

Wladimir G. Boskoff, Bogdan D. Suceavă (2008)

Czechoslovak Mathematical Journal

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

Bargmann representation of q-commutation relations for q > 1 and associated measures

Ilona Królak (2007)

Banach Center Publications

The classical Bargmann representation is given by operators acting on the space of holomorphic functions with the scalar product ⟨ z ⁿ | z k ⟩ q = δ n , k [ n ] q ! = F ( z ⁿ z ̅ k ) . We consider the problem of representing the functional F as a measure for q > 1. We prove the existence of such a measure and investigate some of its properties like uniqueness and radiality. The above problem is closely related to the indeterminate Stieltjes moment problem.

Bases communes holomorphes: nouvelle extension du théorème de Whittaker

Nguyen Thanh Van, Patrice Lassere (1993)

Annales Polonici Mathematici

Résumé. Soient D un ouvert de ℂ et E un compact de D. Moyennant une hypothèse assez faible sur D et ℂ̅ E on montre que si α ∈ ]0,1[ vérifie ∂ D α ⊂ D E , D α étant l’ouvert de niveau z ∈ D : ω(E,D,z) < α, alors toute base commune de O(E) et O(D) est une base de O ( D α ) .

Basic relations valid for the Bernstein spaces B ² σ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, G. Schmeisser (2014)

Banach Center Publications

Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces B σ p are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from B σ p . The difficult situation of derivative-free error estimates is also covered.

Basis of homology adapted to the trigonal automorphism of a Riemann surface.

Helena B. Campos (2007)

RACSAM

A closed (compact without boundary) Riemann surface S of genus g is said to be trigonal if there is a three sheeted covering (a trigonal morphism) from S to the Riemann sphere, ƒ : S →Ĉ. If there is an automorphism of period three, φ, on S permuting the sheets of the covering, we shall call S cyclic trigonal and will be called trigonal automorphism. In this paper we determine the intersection matrix on the first homology group of a cyclic trigonal Riemann surface on an adapted basis B to the trigonal...

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