Smale's Conjecture on Mean Values of Polynomials and Electrostatics

Dimitrov, Dimitar. "Smale's Conjecture on Mean Values of Polynomials and Electrostatics." Serdica Mathematical Journal 33.4 (2007): 399-410. <http://eudml.org/doc/281352>.

@article{Dimitrov2007,
abstract = {2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium related to polynomials with zeros in a ring domain is formulated and discussed.Research supported by the Brazilian foudations CNPq under Grant 304830/2006-2 and FAPESP under Grant 03/01874-2.},
author = {Dimitrov, Dimitar},
journal = {Serdica Mathematical Journal},
keywords = {Zeros of Polynomials; Critical Points; Smale’s Conjecture; Extremal Problem; Electrostatics; zeros of polynomials; critical points; Smale's conjecture; extremal problem; electrostatics},
language = {eng},
number = {4},
pages = {399-410},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Smale's Conjecture on Mean Values of Polynomials and Electrostatics},
url = {http://eudml.org/doc/281352},
volume = {33},
year = {2007},
}

TY - JOUR
AU - Dimitrov, Dimitar
TI - Smale's Conjecture on Mean Values of Polynomials and Electrostatics
JO - Serdica Mathematical Journal
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 33
IS - 4
SP - 399
EP - 410
AB - 2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium related to polynomials with zeros in a ring domain is formulated and discussed.Research supported by the Brazilian foudations CNPq under Grant 304830/2006-2 and FAPESP under Grant 03/01874-2.
LA - eng
KW - Zeros of Polynomials; Critical Points; Smale’s Conjecture; Extremal Problem; Electrostatics; zeros of polynomials; critical points; Smale's conjecture; extremal problem; electrostatics
UR - http://eudml.org/doc/281352
ER -