000 02628nam a22003738i 4500
001 CR9780511543074
003 UkCbUP
005 20200124160233.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090505s2002||||enk o ||1 0|eng|d
020 _a9780511543074 (ebook)
020 _z9780521400688 (hardback)
020 _z9780521102766 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA161.P59
_bS45 2002
082 0 0 _a512.9/42
_221
100 1 _aSheil-Small, T.
_q(Terence),
_d1937-
_eauthor.
245 1 0 _aComplex polynomials /
_cT. Sheil-Small.
264 1 _aCambridge :
_bCambridge University Press,
_c2002.
300 _a1 online resource (xix, 428 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge studies in advanced mathematics ;
_v75
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _a1. The algebra of polynomials -- 2. The degree principle and the fundamental theorem of algebra -- 3. The Jacobian problem -- 4. Analytic and harmonic functions in the unit disc -- 5. Circular regions and Grace's theorem -- 6. The Ilieff-Sendov conjecture -- 7. Self-inversive polynomials -- 8. Duality and an extension of Grace's theorem to rational functions -- 9. Real polynomials -- 10. Level curves -- 11. Miscellaneous topics.
520 _aThis book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis. In fact, throughout the book, the author introduces a variety of ideas and constructs theories around them, incorporating much of the classical theory of polynomials as he proceeds. These ideas are used to study a number of unsolved problems, bearing in mind that such problems indicate the current limitations of our knowledge and present challenges for the future. However, theories also lead to solutions of some problems and several such solutions are given including a comprehensive account of the geometric convolution theory. This is an ideal reference for graduate students and researchers working in this area.
650 0 _aPolynomials.
650 0 _aFunctions of complex variables.
776 0 8 _iPrint version:
_z9780521400688
830 0 _aCambridge studies in advanced mathematics ;
_v75.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511543074
999 _c517793
_d517791