Geometric properties of inverse polynomial images

Klaus Schiefermayr

doi:10.1007/978-1-4614-0772-0_17

Geometric properties of inverse polynomial images

Klaus Schiefermayr

Research Center Wels

Research output: Chapter in Book/Report/Conference proceedings › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

Given a polynomial T_n of degree n, consider the inverse image of R and [-1, 1], denoted by T_n^-1(R) and T_n^-1([-1, 1]), respectively. It is well known that T_n^-1(R) consists of n analytic Jordan arcs moving from ∞ to ∞. In this paper, we give a necessary and sufficient condition such that (1) T_n^-1([-1, 1]) consists of ν analytic Jordan arcs and (2) T_n^-1([-1, 1]) is connected, respectively.

Original language	English
Title of host publication	Approximation Theory XIII
Subtitle of host publication	San Antonio 2010
Pages	277-287
Number of pages	11
DOIs	https://doi.org/10.1007/978-1-4614-0772-0_17
Publication status	Published - 2012
Event	13th International Conference on Approximation Theory, ICAT 2010 - San Antonio, TX, United States Duration: 7 Mar 2010 → 10 Mar 2010

Publication series

Name	Springer Proceedings in Mathematics
Volume	13
ISSN (Print)	2190-5614
ISSN (Electronic)	2190-5622

Conference

Conference	13th International Conference on Approximation Theory, ICAT 2010
Country/Territory	United States
City	San Antonio, TX
Period	07.03.2010 → 10.03.2010

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10.1007/978-1-4614-0772-0_17

Cite this

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title = "Geometric properties of inverse polynomial images",

abstract = "Given a polynomial Tn of degree n, consider the inverse image of R and [-1, 1], denoted by Tn-1(R) and Tn-1([-1, 1]), respectively. It is well known that Tn-1(R) consists of n analytic Jordan arcs moving from ∞ to ∞. In this paper, we give a necessary and sufficient condition such that (1) Tn-1([-1, 1]) consists of ν analytic Jordan arcs and (2) Tn-1([-1, 1]) is connected, respectively.",

author = "Klaus Schiefermayr",

year = "2012",

doi = "10.1007/978-1-4614-0772-0_17",

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series = "Springer Proceedings in Mathematics",

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T1 - Geometric properties of inverse polynomial images

AU - Schiefermayr, Klaus

PY - 2012

Y1 - 2012

N2 - Given a polynomial Tn of degree n, consider the inverse image of R and [-1, 1], denoted by Tn-1(R) and Tn-1([-1, 1]), respectively. It is well known that Tn-1(R) consists of n analytic Jordan arcs moving from ∞ to ∞. In this paper, we give a necessary and sufficient condition such that (1) Tn-1([-1, 1]) consists of ν analytic Jordan arcs and (2) Tn-1([-1, 1]) is connected, respectively.

AB - Given a polynomial Tn of degree n, consider the inverse image of R and [-1, 1], denoted by Tn-1(R) and Tn-1([-1, 1]), respectively. It is well known that Tn-1(R) consists of n analytic Jordan arcs moving from ∞ to ∞. In this paper, we give a necessary and sufficient condition such that (1) Tn-1([-1, 1]) consists of ν analytic Jordan arcs and (2) Tn-1([-1, 1]) is connected, respectively.

UR - http://www.scopus.com/inward/record.url?scp=84869741544&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-0772-0_17

DO - 10.1007/978-1-4614-0772-0_17

M3 - Conference contribution

SN - 9781461407713

T3 - Springer Proceedings in Mathematics

SP - 277

EP - 287

BT - Approximation Theory XIII

T2 - 13th International Conference on Approximation Theory, ICAT 2010

Y2 - 7 March 2010 through 10 March 2010

ER -

Geometric properties of inverse polynomial images

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