Sheil-Small T. — Complex polynomials :: Электронная библиотека попечительского совета мехмата МГУ

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Sheil-Small T. — Complex polynomials

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Название: Complex polynomials

Автор: Sheil-Small T.

Аннотация:

Complex Polynomials explores the geometric theory of polynomials and rational functions in the plane. Early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology, and analysis. 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. Several solutions to problems are given, including a comprehensive account of the geometric convolution theory.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 428

Добавлена в каталог: 07.12.2009

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Предметный указатель

Series representations      125
Shift lemma      69
Shift operator      135
Sign variation      161
Simply-connected domain      35 38 42
Simply-connected surface      89 117
Simultaneous algebraic equations      26
Simultaneous equations      81
Sine polynomial inequality      156
Singularity      27 44
Smale's conjecture      358
Smale's conjecture, Blaschke product approach      365
Smale's conjecture, critical points and minimum points      363
Smale's conjecture, generalisations      367
Smale's conjecture, proof for critical points on circle      361—362
Smale's conjecture, proof for degrees 2, 3, 4      359—360
Smale's conjecture, real critical points      368
Smith, W.      306
Solving algebraic equations      20
Sphere      80
Starlike approximation lemma      276 283
Starlike domain      33
Starlike function condition      275
Starlike, of order 1/2      275
Step function      378
Step function and convex curve      392
Stereographic projection      38 80
Strictly positive operator      138
Strongly real meromorphic function      327
Strongly real meromorphic function, inequality      332
Strongly real meromorphic function, representation theorem      327
Strongly real rational function      319
Strongly real rational function, critical point      321
Strongly real rational function, example      321
Strongly real rational function, positive or negative type      321
Strongly real/interspersion theorem      320
Subordination      168
Subordination inequality      239
Subordination principle      234
Successive derivatives      413
Sudbery's extension      413
Sudbery's theorem      407
Suffridge class      253
Suffridge class, coefficient bound      260
Suffridge class, duality condition      253
Suffridge univalence criterion      243
Suffridge's convolution theorem      254 261
Suffridge's extremal polynomials      251
Suffridge's extremal polynomials, limits      258
Suffridge's theorem, condition for proving containment      257
Suffridge's theorem, proof of part (c)      255
Suffridge, T.J.      241
Summability theory      145
Surface classification theorem      121
Surjectivity, failure of Pinchuk mapping      100
Sylvester determinant      5
Sylvester matrix      10
Sylvester resultant, evaluation      11
Sylvester resultant, exact degree      11
Sylvester resultant, of P-w      11

Sylvester's method of elimination      5
Sylvester's theorem      165
Symmetric linear form      181
Symmetric linear form, Smale's conjecture      359
Symmetric linear form, Walsh's theorem      182
Szegoe's inequality      155
Tangent and argument of curve      387—390
Tangent vector, Jacobian conjecture      89
Tischler, D.      360
Toeplitz theorem      131
Topological argument principle      44
Topology of mapping, Jacobian problem      89
Total variation of argument of curve      389
Trigonometric polynomial      3 50 144
Trigonometric series      125
Two circles theorem      188
Uniqueness theorem      2
Unit disc homeomorphisms      60
Unit disc, zeros      373
Unit element      127 128
Univalence and angular separation of critical points      243
Univalence and bounded boundary rotation      389
Univalence region      197
Univalence sector      200
Univalent polynomials      241
Valence      66 72 84
Variation diminishing      161
Variations in argument/tangent of curve      387—390
Vitushkin, A.G.      118
Walsh's Blaschke product theorem      377
Walsh's theorem on symmetric linear forms      182
Walsh's two circles theorem      188
Walsh, J.L.      305
Weak apolarity      182
Weak Jacobian Conjecture      105
Wilmshurst's conjecture      52
Wilmshurst's example      52
Wilmshurst's method      8
Wilmshurst's theorem      54
Wilmshurst, A.      52 392
Wiman conjecture      343
Winding number      29
Winding number of Jordan curve      46
Winding number properties      34
Wright's theorem      115
Zero cycle      36 41
Zero(s)      22 44
Zero(s) and critical points, self-inversive polynomials      230
Zero(s) of derivatives      407
Zero(s) of second derivative      325
Zero(s) on angular separation condition      248
Zero(s) on argument of polynomial      243
Zero(s) on bounds on coefficients      239
Zero(s) on integral mean/maximum modulus theorem      239
Zero(s) on second angular separation condition      249
Zero(s) on third angular separation condition      251
Zero(s) onzero(s) on unit circle      231
Zero(s), continuity      55
Zero(s), exact number      56
Zero(s), existence of zero path      64
Zero(s), given critical points      201—202

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