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 -