scholarly journals The Filling Discs Dealing with Multiple Values of an Algebroid Function in the Unit Disc

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zu-Xing Xuan ◽  
Nan Wu
Keyword(s):  
Potential Theory ◽  
Finite Order ◽  
Unit Disc ◽  
Algebroid Function

In this paper, by using the potential theory we prove the existence of filling discs dealing with multiple values of an algebroid function of finite order defined in the unit disc.

scholarly journals THE FILLING DISKS OF AN ALGEBROID FUNCTION IN THE UNIT DISK

2010 ◽  
Vol 81 (3) ◽  
pp. 455-464 ◽  
Author(s):  
ZU-XING XUAN
Keyword(s):  
Unit Disk ◽  
Potential Theory ◽  
Finite Order ◽  
Algebroid Function

AbstractUsing potential theory, we prove the existence of filling disks of an algebroid function of finite order defined in the unit disk.

6.—Rationally Convex Hulls and Potential Theory.

1976 ◽  
Vol 74 ◽  
pp. 81-89
Author(s):  
Richard F. Basener
Keyword(s):  
Potential Theory ◽  
Compact Subset ◽  
Unit Disc ◽  
Rational Functions ◽  
Continuous Functions ◽  
Uniform Algebra ◽  
Convex Hulls ◽  
Open Unit ◽  
Open Unit Disc ◽  
Image Position

SynopsisLet S be a compact subset of the open unit disc in C. Associate to S the setLet R(X) be the uniform algebra on X generated by the rational functions which are holomorphic near X. It is shown that the spectrum of R(X) is determined in a simple wayby the potential-theoretic properties of S. In particular, the spectrum of R(X) is X if and only if the functions harmonic near S are uniformly dense in the continuous functions on S. Similar results can be obtained for other subsets of C2 constructed from compact subsets of C.

scholarly journals Finite order solutions of linear differential equations in the unit disc

2009 ◽  
Vol 349 (1) ◽  
pp. 43-54 ◽  
Author(s):  
Risto Korhonen ◽  
Jouni Rättyä
Keyword(s):  
Differential Equations ◽  
Finite Order ◽  
Unit Disc ◽  
Linear Differential Equations ◽  
Linear Differential

scholarly journals ON FILLING DISCS IN THE STRONG BOREL DIRECTION OF ALGEBROID FUNCTION WITH FINITE ORDER

2010 ◽  
Vol 47 (6) ◽  
pp. 1213-1224 ◽  
Author(s):  
Yingying Huo ◽  
Yinying Kong
Keyword(s):  
Finite Order ◽  
Algebroid Function ◽  
Borel Direction

scholarly journals Deficiencies of an entire algebroid function of finite order

1972 ◽  
Vol 24 (1) ◽  
pp. 34-49
Author(s):  
Tsuneo Sato
Keyword(s):  
Finite Order ◽  
Algebroid Function

The Radius of Convexity of a Linear Combination of Functions in or uα

1973 ◽  
Vol 25 (5) ◽  
pp. 982-985
Author(s):  
Douglas Michael Campbell
Keyword(s):  
Linear Combination ◽  
Finite Order ◽  
Convex Functions ◽  
Unit Disc ◽  
Arithmetic Mean ◽  
Geometric Properties ◽  
Radius Of Convexity ◽  
Linear Invariant ◽  
Linear Invariant Family

Labelle and Rahman [4] showed that if f , g ∈ , the normalized convex functions in the unit disc D, then has a radius of convexity at least as large as the smallest root of 1 – 3r + 2r2 — 2r3 = 0. Their method requires neither the properties of the arithmetic mean nor the strong geometric properties of ; indeed, the procedure works for a linear combination of functions from any linear invariant family of finite order.

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

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