A survey of bounds for the zeros of analytic functions obtained by continued fraction methods

Lecture Notes in Mathematics - Rational Approximation and its Applications in Mathematics and Physics ◽

10.1007/bfb0072450 ◽

1987 ◽

pp. 1-23

Author(s):

M. G. De Bruin ◽

J. Gilewicz ◽

H.-J. Runckel

Keyword(s):

Analytic Functions ◽

Continued Fraction ◽

Zeros Of Analytic Functions

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Paths of zeros of analytic functions describing finite quantum systems

Physics Letters A ◽

10.1016/j.physleta.2015.11.032 ◽

2016 ◽

Vol 380 (4) ◽

pp. 548-553

Author(s):

H. Eissa ◽

P. Evangelides ◽

C. Lei ◽

A. Vourdas

Keyword(s):

Analytic Functions ◽

Quantum Systems ◽

Zeros Of Analytic Functions ◽

Finite Quantum Systems

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Inner composition of analytic mappings on the unit disk

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171291000236 ◽

1991 ◽

Vol 14 (2) ◽

pp. 221-226 ◽

Cited By ~ 3

Author(s):

John Gill

Keyword(s):

Fixed Point ◽

Unit Disk ◽

Analytic Functions ◽

Continued Fraction ◽

Unique Fixed Point ◽

Iteration Theory ◽

Basic Theorem ◽

Closed Unit Disk ◽

Compositional Structure ◽

Compositional Structures

A basic theorem of iteration theory (Henrici [6]) states thatfanalytic on the interior of the closed unit diskDand continuous onDwithInt(D)f(D)carries any pointz ϵ Dto the unique fixed pointα ϵ Doff. That is to say,fn(z)→αasn→∞. In [3] and [5] the author generalized this result in the following way: LetFn(z):=f1∘…∘fn(z). Thenfn→funiformly onDimpliesFn(z)λ, a constant, for allz ϵ D. This kind of compositional structure is a generalization of a limit periodic continued fraction. This paper focuses on the convergence behavior of more general inner compositional structuresf1∘…∘fn(z)where thefj's are analytic onInt(D)and continuous onDwithInt(D)fj(D), but essentially random. Applications include analytic functions defined by this process.

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