02455nam a22003378i 4500001001600000003000700016008004100023020001800064020001800082020001800100035002000118041000800138082001700146100002900163245005300192264007100245300003900316336002600355337002600381338003600407490005200443500001300495505043700508520092100945650001701866650003601883856005501919932003201974596000602006949010502012CR9780511543074UkCbUP090505s2002||||enk o ||1 0|eng|d a9780511543074 a9780521400688 a9780521102766 a(Sirsi) a791713 aeng00a512.9/422211 aSheil-Small, T.,eauthor10aComplex polynomialsh[E-Book] /cT. Sheil-Small. 1aCambridge :bCambridge University Press,c2002e(CUP)fCUP20200108 a1 online resource (xix, 428 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aCambridge studies in advanced mathematics ;v75 aenglisch0 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. 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. 0aPolynomials. 0aFunctions of complex variables.40uhttps://doi.org/10.1017/CBO9780511543074zVolltext aCambridgeCore (Order 30059) a1 aXX(791713.1)wAUTOc1i791713-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE