Analytic theory of polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Clarendon Press
2002
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| Edition: | 1. publ. |
| Series: | London Mathematical Society monographs
New series ; 26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 742 S. |
| ISBN: | 0198534930 |
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MARC
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| 100 | 1 | |a Rahman, Qazi I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytic theory of polynomials |c Q. I. Rahman and G. Schmeisser |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press |c 2002 | |
| 300 | |a XIV, 742 S. | ||
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| 490 | 1 | |a London Mathematical Society monographs : New series |v 26 | |
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Record in the Search Index
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| adam_text | ANALYTIC THEORY OF POLYNOMIALS Q. I. RAHMAN UNIVERSITE DE MONTREAL AND
G. SCHMEISSER UNIVERSITAT ERLANGEN -NIIRNBERG CLARENDON PRESS-OXFORD
2002 CONTENTS 1 INTRODUCTION 1 1.1 THE FUNDAMENTAL THEOREM OF ALGEBRA 2
1.2 SYMMETRIC POLYNOMIALS 6 1.3 THE CONTINUITY THEOREM 9 1.4 ORTHOGONAL
POLYNOMIALS: GENERAL PROPERTIES * 13 1.5 THE CLASSICAL ORTHOGONAL
POLYNOMIALS 19 1.6 HARMONIC AND SUBHARMONIC FUNCTIONS 30 1.7 TOOLS FROM
MATRIX ANALYSIS 50 1.8 NOTES 61 I CRITICAL POINTS IN TERMS OF ZEROS
FUNDAMENTAL RESULTS ON CRITICAL POINTS 71 2.1 CONVEX HULLS AND THE
GAUSS-LUCAS THEOREM 71 2.2 EXTENSIONS OF THE GAUSS-LUCAS THEOREM 75 2.3
AVERAGE DISTANCES FROM A LINE OR A POINT 78 2.4 REAL POLYNOMIALS AND
JENSEN S THEOREM * 85 2.5 EXTENSIONS OF JENSEN S THEOREM 88 2.6 NOTES 91
MORE SOPHISTICATED METHODS 96 3.1 CIRCULAR DOMAINS AND POLAR DERIVATIVE
96 3.2 LAGUERRE S THEOREM, ITS VARIANTS, AND APPLICATIONS 98 3.3
APOLARITY 102 3.4 GRACE S THEOREM AND EQUIVALENT FORMS 107 3.5 NOTES 114
MORE SPECIFIC RESULTS ON CRITICAL POINTS 117 4.1 PRODUCTS AND QUOTIENTS
OF POLYNOMIALS 117 4.2 DERIVATIVES OF RECIPROCALS OF POLYNOMIALS 121 4.3
COMPLEX ANALOGUES OF ROLLE S THEOREM 125 4.4 BOUNDS FOR SOME OF THE
CRITICAL POINTS 129 4.5 CONVERSE RESULTS 132 4.6 NOTES 137
APPLICATIONS TO COMPOSITIONS OF POLYNOMIALS 141 5.1 LINEAR COMBINATION
OF RATIONAL FUNCTIONS 142 5.2 COMPLEX ANALOGUES OF THE
INTERMEDIATE-VALUE THEOREM 143 5.3 LINEAR COMBINATION OF DERIVATIVES:
WALSH S APPROACH 148 XII CONTENTS 5.4 LINEAR COMBINATION OF DERIVATIVES:
RECURSIVE APPROACH 151 5.5 MULTIPLICATIVE COMPOSITION: SCHUR-SZEGO
APPROACH 158 5.6 MULTIPLICATIVE COMPOSITION: LAGUERRE S APPROACH 164 5.7
MULTIPLIERS PRESERVING THE REALITY OF ZEROS 172 5.8 NOTES 177 6
POLYNOMIALS WITH REAL ZEROS 184 6.1 THE SPAN OF A POLYNOMIAL 184 6.2
LARGEST ZERO AND LARGEST CRITICAL POINT 189 6.3 INTERLACING AND THE
HERMITE-BIEHLER THEOREM 196 6.4 CONSECUTIVE ZEROS AND CRITICAL POINTS
201 6.5 REFINEMENT OF ROLLE S THEOREM 203 6.6 NOTES 209 7 CONJECTURES
AND SOLUTIONS 212 7.1 A CONJECTURE OF POPOVICIU 212 7.2 A CONJECTURE OF
SMALE 214 7.3 THE CONJECTURE OF SENDOV 224 7.4 NOTES 237 II ZEROS IN
TERMS OF COEFFICIENTS 8 INCLUSION OF ALL ZEROS 243 8.1 THE CAUCHY BOUND
AND ITS ESTIMATES 243 8.2 VARIOUS REFINEMENTS 249 8.3 MULTIPLIERS AND
THE ENESTROM-KAKEYA THEOREM 252 8.4 MORE GENERAL EXPANSIONS 255 8.5
ORTHOGONAL EXPANSIONS WITH REAL COEFFICIENTS 259 8.6 ALTERNATIVE
APPROACH BY MATRIX METHODS 263 8.7 NOTES 270 9 INCLUSION OF SOME OF THE
ZEROS 275 9.1 INCLUSIONS IN TERMS OF A NORM 275 9.2 PELLET S THEOREM AND
ITS CONSEQUENCES 284 9.3 BOUNDS IN TERMS OF SOME OF THE COEFFICIENTS 290
9.4 ORTHOGONAL EXPANSIONS WITH REAL COEFFICIENTS 294 9.5 THE
LANDAU-MONTEL PROBLEM 304 9.6 NOTES 309 10 NUMBER OF ZEROS IN AN
INTERVAL 315 10.1 THE BUDAN-FOURIER THEOREM AND DESCARTES RULE 315 10.2
EXACT COUNT UNDER A SIDE CONDITION 320 10.3 EXTENSIONS TO PAIRS OF
CONJUGATE ZEROS 323 10.4 MORE GENERAL EXPANSIONS 330 10.5 EXACT COUNT BY
STURM SEQUENCES 335 10.6 EXACT COUNT VIA QUADRATIC FORMS 339 10.7 NOTES
350 CONTENTS XIII 11 NUMBER OF ZEROS IN A DOMAIN 357 11.1 GENERAL
PRINCIPLES 357 11.2 NUMBER OF ZEROS IN A SECTOR 359 11.3 NUMBER OF ZEROS
IN A HALF-PLANE 362 11.4 THE ROUTH-HURWITZ PROBLEM 366 11.5 NUMBER OF
ZEROS IN A DISC 374 11.6 DISTRIBUTION OF ZEROS 384 11.7 NOTES 392 III
EXTREMAL PROPERTIES 12 GROWTH ESTIMATES 403 12.1 THE BERNSTEIN-WALSH
LEMMA 403 12.2 THE CONVOLUTION METHOD 408 12.3 THE METHOD OF FUNCTIONALS
416 12.4 VARIOUS REFINEMENTS 428 12.5 LOCAL BEHAVIOUR 447 12.6
EXTENSIONS TO FUNCTIONS OF EXPONENTIAL TYPE 454 12.7 NOTES 456 13 MEAN
VALUES . 460 13.1 MEAN VALUES ON CIRCLES 460 13.2 A CLASS OF LINEAR
OPERATORS 468 13.3 MEAN VALUES ON THE UNIT INTERVAL 486 13.4 NOTES 504
14 DERIVATIVE ESTIMATES ON THE UNIT DISC 508 14.1 BERNSTEIN S INEQUALITY
AND GENERALIZATIONS 508 14.2 REFINEMENTS 515 14.3 CONDITIONS ON THE
COEFFICIENTS 526 14.4 CONDITIONS ON THE ZEROS 532 14.5 SOME SPECIAL
OPERATORS 538 14.6 INEQUALITIES INVOLVING MEAN VALUES 552 14.7 NOTES 557
15 DERIVATIVE ESTIMATES ON THE UNIT INTERVAL 566 15.1 INEQUALITIES OF S.
BERNSTEIN AND A. MARKOV 566 15.2 EXTENSIONS TO HIGHER-ORDER DERIVATIVES
568 15.3 TWO OTHER EXTENSIONS 577 15.4 DEPENDENCE OF THE BOUNDS ON THE
ZEROS 585 15.5 SOME SPECIAL CLASSES 601 15.6 L P ANALOGUES OF MARKOV S
INEQUALITY 611 15.7 NOTES 622 XIV CONTENTS 16 COEFFICIENT ESTIMATES 636
16.1 POLYNOMIALS ON THE UNIT CIRCLE 636 16.2 COEFFICIENTS OF REAL
TRIGONOMETRIC POLYNOMIALS 653 16.3 POLYNOMIALS ON THE UNIT INTERVAL 672
16.4 NOTES 677 REFERENCES 681 LIST OF NOTATION 729 INDEX 733
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| any_adam_object | 1 |
| author | Rahman, Qazi I. |
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| ctrlnum | (OCoLC)248267285 (DE-599)BVBBV014016355 |
| dewey-full | 512.942 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.942 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T18:56:10Z |
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| isbn | 0198534930 |
| language | English |
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| physical | XIV, 742 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Clarendon Press |
| record_format | marc |
| series | London Mathematical Society monographs |
| series2 | London Mathematical Society monographs : New series |
| spelling | Rahman, Qazi I. Verfasser aut Analytic theory of polynomials Q. I. Rahman and G. Schmeisser 1. publ. Oxford [u.a.] Clarendon Press 2002 XIV, 742 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society monographs : New series 26 Polynom - Analytische Funktion Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Polynom (DE-588)4046711-9 s Funktionentheorie (DE-588)4018935-1 s DE-604 Schmeißer, Gerhard Sonstige oth London Mathematical Society monographs New series ; 26 (DE-604)BV045355493 26 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009596710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rahman, Qazi I. Analytic theory of polynomials London Mathematical Society monographs Polynom - Analytische Funktion Funktionentheorie (DE-588)4018935-1 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4046711-9 |
| title | Analytic theory of polynomials |
| title_auth | Analytic theory of polynomials |
| title_exact_search | Analytic theory of polynomials |
| title_full | Analytic theory of polynomials Q. I. Rahman and G. Schmeisser |
| title_fullStr | Analytic theory of polynomials Q. I. Rahman and G. Schmeisser |
| title_full_unstemmed | Analytic theory of polynomials Q. I. Rahman and G. Schmeisser |
| title_short | Analytic theory of polynomials |
| title_sort | analytic theory of polynomials |
| topic | Polynom - Analytische Funktion Funktionentheorie (DE-588)4018935-1 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Polynom - Analytische Funktion Funktionentheorie Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009596710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
| work_keys_str_mv | AT rahmanqazii analytictheoryofpolynomials AT schmeißergerhard analytictheoryofpolynomials |