Computing zeros of analytic mappings: A logarithmic residue approach

1998 ◽  
Vol 38 (3) ◽  
pp. 583-596
Author(s):  
P. Kravanja ◽  
R. Cools ◽  
A. Haegemans
Keyword(s):  
Logarithmic Residue ◽  
Analytic Mappings

scholarly journals Hardy Spaces for Quasiregular Mappings and Composition Operators

2021 ◽  
Author(s):  
Tomasz Adamowicz ◽  
María J. González
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Quasiconformal Mappings ◽  
Carleson Measures ◽  
Quasiregular Mappings ◽  
Classical Setting ◽  
Appl Math ◽  
Analytic Mappings

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

scholarly journals Fixed points of quasi-nonexpansive mappings

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Linear Space ◽  
Complex Plane ◽  
Normed Linear Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
The Other ◽  
Commuting Mappings ◽  
Analytic Mappings

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

Finite Laurent Developments and the Logarithmic Residue Theorem in the Real Non-analytic Case

2005 ◽  
Vol 51 (4) ◽  
pp. 519-552 ◽  
Author(s):  
Julián López-Gómez ◽  
Carlos Mora-Corral
Keyword(s):  
Residue Theorem ◽  
The Real ◽  
Analytic Case ◽  
Logarithmic Residue

Analytic Mappings

1968 ◽  
pp. 211-231
Author(s):  
Burton Rodin ◽  
Leo Sario
Keyword(s):  
Analytic Mappings

scholarly journals Remarks on the existence of analytic mappings

1970 ◽  
Vol 22 (2) ◽  
pp. 172-177
Author(s):  
Mitsuru Ozawa
Keyword(s):  
Analytic Mappings

scholarly journals Growth Theorems for a Subclass of Strongly Spirallike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yan-Yan Cui ◽  
Chao-Jun Wang ◽  
Si-Feng Zhu
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Starlike Functions ◽  
Geometric Properties ◽  
Strongly Starlike Functions ◽  
Strongly Starlike ◽  
Spirallike Functions ◽  
Analytic Mappings

In this paper we consider a subclass of strongly spirallike functions on the unit diskDin the complex planeC, namely, strongly almost spirallike functions of typeβand orderα. We obtain the growth results for strongly almost spirallike functions of typeβand orderαon the unit diskDinCby using subordination principles and the geometric properties of analytic mappings. Furthermore we get the growth theorems for strongly almost starlike functions of orderαand strongly starlike functions on the unit diskDofC. These growth results follow the deviation results of these functions.

Local complexity growth for iterations of real analytic mappings and semicontinuity moduli of the entropy

1991 ◽  
Vol 11 (3) ◽  
pp. 583-602 ◽  
Author(s):  
Y. Yomdin
Keyword(s):  
Local Complexity ◽  
Real Analytic ◽  
Analytic Mappings

AbstractWe consider some ways in which regularity of a mapping influences dynamics of its iterations and growth of various complexity-type invariants.

scholarly journals Poles of Archimedean zeta functions for analytic mappings

2012 ◽  
Vol 87 (1) ◽  
pp. 1-21 ◽  
Author(s):  
E. León-Cardenal ◽  
Willem Veys ◽  
W. A. Zúñiga-Galindo
Keyword(s):  
Zeta Functions ◽  
Analytic Mappings

Fitting ideals and multiple points of analytic mappings

1989 ◽  
pp. 107-161 ◽  
Author(s):  
David Mond ◽  
Ruud Pellikaan
Keyword(s):  
Multiple Points ◽  
Analytic Mappings
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