TY - GEN

T1 - Geometric properties of inverse polynomial images

AU - Schiefermayr, Klaus

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

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 -