Discrepancy of signed measures and polynomial approximation:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2002
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 438 S. Ill. |
| ISBN: | 0387986529 |
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Record in the Search Index
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| adam_text | VLADIMIR V. ANDRIEVSKII HANS-PETER BLATT DISCREPANCY OF SIGNED MEASURES
AND POLYNOMIAL APPROXIMATION SPRINGER CONTENTS PREFACE VII AUXILIARY
FACTS 1 1.1 BASIC POTENTIAL-THEORETICAL CONCEPTS 1 1.1.1 SETS AND CURVES
1 1.1.2 HARMONIC AND SUBHARMONIC FUNCTIONS, MAXIMUM PRINCIPLE 2 1.1.3
GREEN S FORMULA 6 1.1.4 HARMONIC MEASURE 8 1.1.5 ENERGY, CAPACITY,
EQUILIBRIUM MEASURE 10 1.1.6 MAXIMUM PRINCIPLE 14 1.1.7 WEAK* TOPOLOGY,
HELLY S THEOREM 14 1.1.8 GREEN S FUNCTION 14 1.1.9 FEKETE POINTS,
TRANSFINITE DIAMETER, CHEBYSHEV CONSTANT 17 1.2 CONFORMAL AND
QUASICONFORMAL MAPPINGS 19 1.2.1 BASIC PRINCIPLES OF COMPLEX ANALYSIS 19
1.2.2 EQUILIBRIUM MEASURE AND CONFORMAL MAPPINGS ... 21 1.2.3 DISTORTION
THEOREMS 22 1.2.4 MODULE OF A FAMILY OF CURVES AND ARCS 24 1.2.5
QUASICONFORMAL CURVES AND ARCS 27 1.2.6 DINI-SMOOTH CURVES AND ARCS 32
1.3 FABER POLYNOMIALS AND GRUNSKY COEFFICIENTS 37 1.4 MONIC POLYNOMIALS
40 1.5 LINEAR APPROXIMATION 44 1.5.1 POLYNOMIAL APPROXIMATION 45 1.5.2
AVERAGING AND SMOOTHING 46 1.6 ORDERING SYMBOLS 48 1.7 HISTORICAL
COMMENTS 48 XII CONTENTS 2 ZERO DISTRIBUTION OF POLYNOMIALS 49 2.1
JENTZSCH-SZEGO TYPE THEOREMS 50 2.2 ERDOS-TURAN TYPE THEOREMS FOR
QUASICONFORMAL CURVES AND ARCS 56 2.2.1 POLYNOMIAL BOUNDS ON
QUASICONFORMAL CURVES ... 57 2.2.2 POLYNOMIAL BOUNDS ON QUASICONFORMAL
ARCS 68 2.3 SHARPNESS AND EXTENSIONS OF ERDOS-TURAN TYPE THEOREMS . 72
2.4 ERDOS-TURAN TYPE THEOREMS ON COMPACT SETS WITH SMOOTH CURVES AND
ARCS 78 2.5 ERDOS-TURAN TYPE THEOREMS ON A SYSTEM OF INTERVALS ... 86
2.6 HISTORICAL COMMENTS 92 3 DISCREPANCY THEOREMS VIA TWO*SIDED BOUNDS
FOR POTENTIALS 95 3.1 ESTIMATES FOR QUASICONFORMAL CURVES AND ARCS 96
3.2 LOCAL ESTIMATES FOR INTERVALS 108 3.3 LOCAL ESTIMATES FOR
DINI-SMOOTH ARCS AND CURVES 114 3.4 HISTORICAL COMMENTS 128 4
DISCREPANCY THEOREMS VIA ONE-SIDED BOUNDS FOR POTENTIALS 129 4.1 OUTER
BOUNDS FOR POTENTIALS 130 4.2 INNER AND OUTER BOUNDS FOR POTENTIALS 150
4.3 INNER BOUNDS FOR POTENTIALS OF SIGNED MEASURES ON ANALYTIC JORDAN
CURVES 152 4.4 ANOTHER APPROACH FOR DINI-SMOOTH ARCS 161 4.5 HISTORICAL
COMMENTS 172 5 DISCREPANCY THEOREMS VIA ENERGY INTEGRALS 173 5.1 MODULUS
OF A DOUBLY SPLIT PLANE 174 5.2 ESTIMATES OF MASS DISTRIBUTIONS FROM
THEIR ENERGIES . . . . 178 5.3 HISTORICAL COMMENTS 186 6 APPLICATIONS OF
JENTZSCH-SZEGO AND ERDOS-TURAN TYPE THEOREMS 187 6.1 POLYNOMIALS OF BEST
UNIFORM APPROXIMATION 188 6.2 POLYNOMIALS OF NEAR-BEST APPROXIMATION 193
6.3 POLYNOMIALS OF MAXIMAL CONVERGENCE 202 6.4 A-VALUES OF ORTHOGONAL
POLYNOMIALS ON QUASIDISKS 208 6.5 ZEROS OF BIEBERBACH POLYNOMIALS AND
THEIR DERIVATIVES . . . 215 6.6 HISTORICAL COMMENTS 223 7 APPLICATIONS
OF DISCREPANCY THEOREMS 225 7.1 DISTRIBUTION OF FEKETE POINTS 226 7.2
FEKETE POINTS FOR DOMAINS WITH ANALYTIC BOUNDARY 229 CONTENTS XIII 7.3
EXTREME POINTS IN UNIFORM POLYNOMIAL APPROXIMATION . . . 241 7.4
ALTERNATION POINTS IN CHEBYSHEV APPROXIMATION 248 7.5 SIGN CHANGES IN L
P - APPROXIMATION 254 7.5.1 THE CASE 1 P OO 256 7.5.2 THE CASE P = 1
266 7.6 EXTREMAL POLYNOMIALS ON THE REAL LINE 274 7.7 ZEROS OF
ORTHOGONAL POLYNOMIALS 297 7.7.1 ORTHOGONAL POLYNOMIALS ON REAL
INTERVALS 297 7.7.2 ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE 312 7.8
HISTORICAL COMMENTS 317 8 SPECIAL TOPICS 321 8.1 POLYNOMIAL
APPROXIMATION TO A PIECEWISE ANALYTIC FUNCTION ON TOUCHING DOMAINS 321
8.2 UNIFORM CONVERGENCE OF BIEBERBACH POLYNOMIALS IN DOMAINS WITH
QUASICONFORMAL BOUNDARY 336 8.3 HISTORICAL COMMENTS 340 A CONFORMALLY
INVARIANT CHARACTERISTICS OF CURVE FAMILIES 341 A.I MODULE AND EXTREMAL
LENGTH OF A CURVE FAMILY 341 A.2 REDUCED MODULE 357 B BASICS IN THE
THEORY OF QUASICONFORMAL MAPPINGS 361 B.I QUASICONFORMAL MAPPINGS . .
361 B.2 QUASICONFORMAL CURVES AND ARCS 369 C CONSTRUCTIVE THEORY OF
FUNCTIONS OF A COMPLEX VARIABLE 381 C.I JACKSON TYPE KERNELS 383 C.2
POLYNOMIAL KERNELS APPROXIMATING THE CAUCHY KERNEL . . . 386 C.3 INVERSE
THEOREMS 393 C.4 POLYNOMIAL APPROXIMATION IN DOMAINS WITH SMOOTH
BOUNDARY 403 D MISCELLANEOUS TOPICS 407 D.I THE REGULARIZED DISTANCE 407
D.2 GREEN S FUNCTION FOR A SYSTEM OF INTERVALS 409 BIBLIOGRAPHY 415
NOTATION 427 INDEX 435
|
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| author | Andrievskii, Vladimir V. Blatt, Hans-Peter |
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| spelling | Andrievskii, Vladimir V. Verfasser aut Discrepancy of signed measures and polynomial approximation Vladimir V. Andrievskii ; Hans-Peter Blatt New York [u.a.] Springer 2002 XIII, 438 S. Ill. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Approximation, Théorie de l' Polynômes orthogonaux Approximation theory Orthogonal polynomials Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Polynomapproximation (DE-588)4197097-4 gnd rswk-swf Maß Mathematik (DE-588)4037856-1 gnd rswk-swf Diskrepanz (DE-588)4499634-2 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s DE-604 Approximationstheorie (DE-588)4120913-8 s Potenzialtheorie (DE-588)4046939-6 s Maß Mathematik (DE-588)4037856-1 s Diskrepanz (DE-588)4499634-2 s Polynomapproximation (DE-588)4197097-4 s Blatt, Hans-Peter Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009666902&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andrievskii, Vladimir V. Blatt, Hans-Peter Discrepancy of signed measures and polynomial approximation Approximation, Théorie de l' Polynômes orthogonaux Approximation theory Orthogonal polynomials Potenzialtheorie (DE-588)4046939-6 gnd Orthogonale Polynome (DE-588)4172863-4 gnd Polynomapproximation (DE-588)4197097-4 gnd Maß Mathematik (DE-588)4037856-1 gnd Diskrepanz (DE-588)4499634-2 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4172863-4 (DE-588)4197097-4 (DE-588)4037856-1 (DE-588)4499634-2 (DE-588)4120913-8 |
| title | Discrepancy of signed measures and polynomial approximation |
| title_auth | Discrepancy of signed measures and polynomial approximation |
| title_exact_search | Discrepancy of signed measures and polynomial approximation |
| title_full | Discrepancy of signed measures and polynomial approximation Vladimir V. Andrievskii ; Hans-Peter Blatt |
| title_fullStr | Discrepancy of signed measures and polynomial approximation Vladimir V. Andrievskii ; Hans-Peter Blatt |
| title_full_unstemmed | Discrepancy of signed measures and polynomial approximation Vladimir V. Andrievskii ; Hans-Peter Blatt |
| title_short | Discrepancy of signed measures and polynomial approximation |
| title_sort | discrepancy of signed measures and polynomial approximation |
| topic | Approximation, Théorie de l' Polynômes orthogonaux Approximation theory Orthogonal polynomials Potenzialtheorie (DE-588)4046939-6 gnd Orthogonale Polynome (DE-588)4172863-4 gnd Polynomapproximation (DE-588)4197097-4 gnd Maß Mathematik (DE-588)4037856-1 gnd Diskrepanz (DE-588)4499634-2 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Approximation, Théorie de l' Polynômes orthogonaux Approximation theory Orthogonal polynomials Potenzialtheorie Orthogonale Polynome Polynomapproximation Maß Mathematik Diskrepanz Approximationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009666902&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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