Constructive approximation: advanced problems
Gespeichert in:
Hauptverfasser: | , , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin [u.a.]
Springer
1996
|
Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
304 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XI, 649 S. |
ISBN: | 0387570284 3540570284 9783642646102 |
Internformat
MARC
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100 | 1 | |a Lorentz, George G. |d 1910-2006 |e Verfasser |0 (DE-588)119043750 |4 aut | |
245 | 1 | 0 | |a Constructive approximation |b advanced problems |c George G. Lorentz ; Manfred v. Golitschek ; Yuly Makovoz |
264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
300 | |a XI, 649 S. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 304 | |
650 | 4 | |a Approximation, Théorie de l' | |
650 | 7 | |a Approximation, théorie de l' |2 ram | |
650 | 7 | |a Fourier-analyse |2 gtt | |
650 | 7 | |a approximation Padé |2 inriac | |
650 | 7 | |a approximation avec contrainte |2 inriac | |
650 | 7 | |a approximation polynomiale |2 inriac | |
650 | 7 | |a approximation rationnelle |2 inriac | |
650 | 7 | |a espace fonction |2 inriac | |
650 | 7 | |a fonction spline |2 inriac | |
650 | 7 | |a ondelette orthogonale |2 inriac | |
650 | 7 | |a polynôme Chebyshev |2 inriac | |
650 | 7 | |a polynôme trigonométrique |2 inriac | |
650 | 7 | |a théorie approximation |2 inriac | |
650 | 7 | |a théorème Weierstrass |2 inriac | |
650 | 4 | |a Approximation theory | |
650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
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700 | 1 | |a Golitschek, Manfred von |e Verfasser |4 aut | |
700 | 1 | |a Makovoz, Yuly |e Verfasser |4 aut | |
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Datensatz im Suchindex
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adam_text | GEORGE G.LORENTZ
MANFRED V. GOLITSCHEK
YULY MAKOVOZ
CONSTRUCTIVE
APPROXIMATION
ADVANCED PROBLEMS
WITH 10 FIGURES
SPRINGE
R
CONTENT
S
CHAPTE
R 1. PROBLEM
S OF POLYNOMIA
L APPROXIMATIO
N 1
§ 1. EXAMPLE
S OF POLYNOMIAL
S OF BEST APPROXIMATIO
N 1
§ 2. DISTRIBUTIO
N OF ALTERNATIO
N POINT
S OF POLYNOMIAL
S
OF BES
T APPROXIMATIO
N 4
§ 3. DISTRIBUTIO
N OF ZEROS OF POLYNOMIAL
S OF BEST APPROXIMATIO
N ...
. 11
§ 4. ERRO
R OF APPROXIMATIO
N 20
§ 5. APPROXIMATIO
N ON (-OO, OO) BY LINEAR COMBINATION
S
OF FUNCTION
S (X - C)~
L
23
§ 6. WEIGHTED APPROXIMATIO
N BY POLYNOMIAL
S ON (-OO, OO) 28
§ 7. SPACES OF APPROXIMATIO
N THEOR
Y 33
§ 8. PROBLEM
S AN
D NOTE
S 37
CHAPTE
R 2. APPROXIMATIO
N PROBLEM
S WIT
H CONSTRAINT
S 39
§ 1. INTRODUCTIO
N 39
§ 2. GROWT
H RESTRICTION
S FOR TH
E COEFFICIENTS 39
§ 3. MONOTON
E APPROXIMATIO
N 43
§ 4. POLYNOMIAL
S WIT
H INTEGRA
L COEFFICIENTS 49
§ 5. DETERMINATIO
N OF TH
E CHARACTERISTI
C SETS 59
§ 6. MARKOV-TYP
E INEQUALITIE
S 64
§ 7. TH
E INEQUALIT
Y OF REMEZ 73
§ 8. ONE-SIDED APPROXIMATIO
N BY POLYNOMIAL
S 76
§ 9. PROBLEM
S 81
§ 10. NOTE
S 82
CHAPTE
R 3. INCOMPLET
E POLYNOMIAL
S 85
§ 1. INCOMPLET
E POLYNOMIAL
S 85
§ 2. INCOMPLET
E CHEBYSHE
V POLYNOMIAL
S 89
§ 3. INCOMPLET
E TRIGONOMETRI
C POLYNOMIAL
S 92
§ 4. SEQUENCES OF POLYNOMIAL
S WIT
H MAN
Y REAL ZEROS 98
§ 5. PROBLEM
S 104
§ 6. NOTE
S 104
VIII CONTENTS
CHAPTE
R 4. WEIGHTED POLYNOMIAL
S 105
§ 1. ESSENTIA
L SET
S OF WEIGHTED POLYNOMIAL
S 105
§ 2. WEIGHTED CHEBYSHE
V POLYNOMIAL
S 109
§ 3. TH
E EQUILIBRIU
M MEASUR
E 117
§ 4. DETERMINATIO
N OF MINIMA
L ESSENTIA
L SETS 125
§ 5. WEIERSTRAS
S THEOREM
S AN
D OSCILLATIONS 131
§ 6. WEIERSTRAS
S THEORE
M FOR FREU
D WEIGHTS 134
§ 7. PROBLEM
S 141
§ 8. NOTES 141
CHAPTE
R 5. WAVELETS AN
D ORTHOGONA
L EXPANSION
S 145
§ 1. MULTIRESOLUTION
S AN
D WAVELETS 145
§ 2. SCALING FUNCTION
S WIT
H A MONOTON
E MAJORAN
T 151
§ 3. PERIODIZATIO
N 156
§ 4. POLYNOMIA
L SCHAUDE
R BASES 160
§ 5. ORTHONORMA
L POLYNOMIA
L BASES 164
§ 6. PROBLEM
S AN
D NOTE
S 172
CHAPTE
R 6. SPLINES 175
§ 1. GENERA
L FACT
S 175
§ 2. SPLINES OF BES
T APPROXIMATIO
N 181
§ 3. PERIODI
C SPLINES 189
§ 4. CONVERGENCE OF SOME SPLINE OPERATOR
S 196
§ 5. NOTE
S 202
CHAPTE
R 7. RATIONA
L APPROXIMATIO
N 205
§ 1. INTRODUCTIO
N 205
§ 2. BES
T RATIONA
L APPROXIMATIO
N 210
§ 3. RATIONA
L APPROXIMATIO
N OF |X
| 217
§ 4. APPROXIMATIO
N OF E
X
ON [-1,1
] 221
§ 5. RATIONA
L APPROXIMATIO
N OF E~
X
ON [0, OO) 227
§ 6. APPROXIMATIO
N OF CLASSES OF FUNCTION
S 231
§ 7. THEOREM
S OF POPO
V 235
§ 8. PROPERTIE
S OF TH
E OPERATO
R OF BES
T RATIONA
L APPROXIMATIO
N
IN YY AN
D L
P
242
§ 9. APPROXIMATIO
N BY RATIONA
L FUNCTION
S WIT
H ARBITRAR
Y POWERS ..
. 248
§ 10. PROBLEM
S 251
§ 11
. NOTE
S 252
CHAPTE
R 8. STAHL
S THEORE
M 255
§ 1. INTRODUCTIO
N AN
D MAI
N RESUL
T 255
§ 2. A DIRICHLET PROBLE
M ON [1/2
, L/P
N
] 256
CONTENTS IX
§ 3. TH
E SECOND APPROAC
H T
O TH
E DIRICHLET PROBLE
M 263
§ 4. PROO
F OF THEORE
M 1.1 271
§ 5. NOTE
S 276
CHAPTE
R 9. PAD
E APPROXIMATIO
N 277
§1
. TH
E PAD
E TABL
E 277
§ 2. CONVERGENCE OF TH
E ROWS OF TH
E PAD
E TABL
E 282
§ 3. TH
E NUTTALL-POMMERENK
E THEORE
M 290
§ 4. PROBLEM
S 296
§ 5. NOTE
S 296
CHAPTE
R 10. HARD
Y SPACE METHOD
S IN RATIONA
L APPROXIMATIO
N 299
§ 1. BERNSTEIN-TYP
E INEQUALITIE
S FOR RATIONA
L FUNCTION
S 300
§ 2. UNIFORM RATIONA
L APPROXIMATIO
N I
N HARD
Y SPACES 308
§ 3. APPROXIMATIO
N BY SIMPLE FUNCTION
S 314
§ 4. TH
E JACKSON-RUSA
K OPERATOR
; RATIONA
L APPROXIMATIO
N
OF SUM
S OF SIMPLE FUNCTION
S 320
§ 5. RATIONA
L APPROXIMATIO
N ON T AN
D ON [-1,1] 322
§ 6. RELATION
S BETWEE
N SPLINE AN
D RATIONA
L APPROXIMATIO
N
I
N TH
E SPACE
S L
P
, 0 P OO 332
§ 7. PROBLEM
S 341
§ 8. NOTE
S 341
CHAPTE
R 11
. MIINT
Z POLYNOMIAL
S 345
§ 1. DEFINITIONS AN
D SIMPLE PROPERTIE
S 345
§ 2. MIINTZ-JACKSO
N THEOREM
S 347
§ 3. A
N INVERS
E MIINTZ-JACKSO
N THEORE
M 353
§ 4. TH
E INDE
X OF APPROXIMATIO
N 360
§ 5. MARKOV-TYP
E INEQUALIT
Y FOR MIINTZ POLYNOMIAL
S 362
§ 6. PROBLEM
S 365
§ 7. NOTE
S 366
CHAPTE
R 12. NONLINEA
R APPROXIMATIO
N 369
§ 1. DEFINITIONS AN
D SIMPLE PROPERTIE
S 369
§ 2. VARISOLVENT FAMILIES 371
§ 3. EXPONENTIA
L SUM
S 376
§ 4. LOWER BOUND
S FOR ERROR
S OF NONLINEA
R APPROXIMATIO
N 383
§ 5. CONTINUOU
S SELECTIONS FROM METRI
C PROJECTION
S 386
§ 6. APPROXIMATIO
N I
N BANAC
H SPACES: SUN
S AN
D CHEBYSHE
V SET
S ...
. 390
§ 7. PROBLEM
S 395
§ 8. NOTE
S 396
X CONTENTS
CHAPTE
R 13. WIDTH
S I 399
§ 1. DEFINITIONS AN
D BASIC PROPERTIE
S 399
§ 2. RELATIONS BETWEE
N DIFFERENT WIDTH
S 407
§ 3. WIDTH
S OF CUBE
S AN
D OCTAHEDR
A 410
§ 4. WIDTH
S IN HILBER
T SPACES 412
§ 5. APPLICATIONS OF BORSUK
S THEORE
M 418
§ 6. VARIATIONAL PROBLEM
S AN
D SPECTRA
L FUNCTION
S 423
§ 7. RESULTS OF BUSLAEV AN
D TIKHOMIRO
V 432
§ 8. CLASSES OF DIFFERENTIABLE FUNCTION
S ON A
N INTERVA
L 441
§ 9. CLASSES OF ANALYTI
C FUNCTION
S 443
§ 10. PROBLEMS 445
§ 11. NOTES 447
CHAPTER 14. WIDTH
S II
: WEAK ASYMPTOTIC
S FOR WIDTH
S
OF LIPSCHITZ BALLS, RANDO
M APPROXIMANT
S 449
§ 1. INTRODUCTIO
N 449
§ 2. DISCRETIZATION 451
§ 3. WEAK EQUIVALENCES FOR WIDTHS
. ELEMENTAR
Y METHOD
S 453
§ 4. DISTRIBUTIO
N OF SCALAR PRODUCT
S OF UNI
T VECTORS 461
§ 5. KASHIN S THEOREM
S 465
§ 6. GAUSSIAN MEASURES 469
§ 7. LINEAR WIDTH
S OF FINIT
E DIMENSIONAL BALLS 472
§ 8. LINEAR WIDTH
S OF TH
E LIPSCHITZ CLASSES 478
§ 9. PROBLEMS 481
§ 10. NOTES 481
CHAPTER 15. ENTROP
Y 485
§ 1. ENTROP
Y AN
D CAPACIT
Y 485
§ 2. ELEMENTARY ESTIMATE
S 489
§ 3. LINEAR APPROXIMATIO
N AN
D ENTROP
Y 492
§ 4. RELATIONS BETWEEN ENTROP
Y AN
D WIDTH
S 497
§ 5. ENTROPY OF CLASSES OF ANALYTI
C FUNCTION
S 502
§ 6. THE BIRMAN-SOLOMYAK THEORE
M 506
§ 7. ENTROPY NUMBER
S OF OPERATOR
S 509
§ 8. NOTES 514
CHAPTE
R 16. CONVERGENCE OF SEQUENCES OF OPERATOR
S 517
§ 1. INTRODUCTIO
N 517
§ 2. SIMPLE NECESSARY AN
D SUFFICIENT CONDITION
S 518
§ 3. GEOMETRIC PROPERTIE
S OF DOMINATIN
G SETS 523
§ 4. STRICT DOMINATIN
G SYSTEMS
; MINIMAL SYSTEMS; EXAMPLE
S 528
§ 5. SHADOWS OF SETS OF CONTINUOU
S FUNCTION
S 536
§ 6. SHADOWS IN BANAC
H FUNCTIO
N SPACES 541
CONTENT
S X
I
§ 7. POSITIV
E CONTRACTION
S 545
§ 8. CONTRACTION
S 547
§ 9. NOTE
S 551
CHAPTE
R 17. REPRESENTATIO
N OF FUNCTION
S BY SUPERPOSITION
S 553
§ 1. TH
E THEOREM
S OF KOLMOGOROV 553
§ 2. PROO
F OF TH
E THEOREM
S 555
§ 3. FUNCTION
S NO
T REPRESENTABL
E BY SUPERPOSITION
S 559
§ 4. LINEAR SUPERPOSITION
S 562
§ 5. NOTE
S 564
APPENDI
X 1. THEOREM
S OF BORSUK AN
D OF BRUNN-MINKOWSKI 567
§ 1. BORSUK
S THEORE
M 567
§ 2. TH
E BRUNN-MINKOWSK
I INEQUALIT
Y 572
APPENDI
X 2. ESTIMATE
S OF SOME ELLIPTI
C INTEGRAL
S 575
APPENDI
X 3
. HARD
Y SPACES AN
D BLASCHKE PRODUCT
S 581
§ 1. HARD
Y SPACES 581
§ 2. CONJUGAT
E FUNCTION
S AN
D CAUCH
Y INTEGRAL
S 584
§ 3. ATOMI
C DECOMPOSITION
S IN HARD
Y SPACES 587
§ 4. BLASCHKE PRODUCT
S 591
APPENDI
X 4. POTENTIA
L THEOR
Y AN
D LOGARITHMI
C CAPACIT
Y 595
§ 1. LOGARITHMI
C POTENTIAL
S 595
§ 2. EQUILIBRIU
M DISTRIBUTIO
N AN
D LOGARITHMI
C CAPACIT
Y 603
§ 3. TH
E DIRICHLET PROBLE
M AN
D GREEN
S FUNCTIO
N 614
§ 4. BALAYAG
E METHOD
S 615
BIBLIOGRAPH
Y 621
AUTHO
R INDE
X 641
SUBJEC
T INDE
X 647
|
any_adam_object | 1 |
author | Lorentz, George G. 1910-2006 Golitschek, Manfred von Makovoz, Yuly |
author_GND | (DE-588)119043750 |
author_facet | Lorentz, George G. 1910-2006 Golitschek, Manfred von Makovoz, Yuly |
author_role | aut aut aut |
author_sort | Lorentz, George G. 1910-2006 |
author_variant | g g l gg ggl m v g mv mvg y m ym |
building | Verbundindex |
bvnumber | BV010616593 |
callnumber-first | Q - Science |
callnumber-label | QA221 |
callnumber-raw | QA221 |
callnumber-search | QA221 |
callnumber-sort | QA 3221 |
callnumber-subject | QA - Mathematics |
classification_rvk | SK 470 SK 905 |
classification_tum | MAT 410f |
ctrlnum | (OCoLC)34149995 (DE-599)BVBBV010616593 |
dewey-full | 515/.83 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515/.83 |
dewey-search | 515/.83 |
dewey-sort | 3515 283 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV010616593 |
illustrated | Not Illustrated |
indexdate | 2024-07-09T17:56:03Z |
institution | BVB |
isbn | 0387570284 3540570284 9783642646102 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007082899 |
oclc_num | 34149995 |
open_access_boolean | |
owner | DE-20 DE-355 DE-BY-UBR DE-12 DE-384 DE-703 DE-739 DE-824 DE-29T DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
owner_facet | DE-20 DE-355 DE-BY-UBR DE-12 DE-384 DE-703 DE-739 DE-824 DE-29T DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
physical | XI, 649 S. |
publishDate | 1996 |
publishDateSearch | 1996 |
publishDateSort | 1996 |
publisher | Springer |
record_format | marc |
series | Grundlehren der mathematischen Wissenschaften |
series2 | Grundlehren der mathematischen Wissenschaften |
spelling | Lorentz, George G. 1910-2006 Verfasser (DE-588)119043750 aut Constructive approximation advanced problems George G. Lorentz ; Manfred v. Golitschek ; Yuly Makovoz Berlin [u.a.] Springer 1996 XI, 649 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 304 Approximation, Théorie de l' Approximation, théorie de l' ram Fourier-analyse gtt approximation Padé inriac approximation avec contrainte inriac approximation polynomiale inriac approximation rationnelle inriac espace fonction inriac fonction spline inriac ondelette orthogonale inriac polynôme Chebyshev inriac polynôme trigonométrique inriac théorie approximation inriac théorème Weierstrass inriac Approximation theory Approximation (DE-588)4002498-2 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s DE-604 Approximation (DE-588)4002498-2 s 1\p DE-604 Golitschek, Manfred von Verfasser aut Makovoz, Yuly Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-60932-9 Grundlehren der mathematischen Wissenschaften 304 (DE-604)BV000000395 304 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007082899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Lorentz, George G. 1910-2006 Golitschek, Manfred von Makovoz, Yuly Constructive approximation advanced problems Grundlehren der mathematischen Wissenschaften Approximation, Théorie de l' Approximation, théorie de l' ram Fourier-analyse gtt approximation Padé inriac approximation avec contrainte inriac approximation polynomiale inriac approximation rationnelle inriac espace fonction inriac fonction spline inriac ondelette orthogonale inriac polynôme Chebyshev inriac polynôme trigonométrique inriac théorie approximation inriac théorème Weierstrass inriac Approximation theory Approximation (DE-588)4002498-2 gnd Approximationstheorie (DE-588)4120913-8 gnd |
subject_GND | (DE-588)4002498-2 (DE-588)4120913-8 |
title | Constructive approximation advanced problems |
title_auth | Constructive approximation advanced problems |
title_exact_search | Constructive approximation advanced problems |
title_full | Constructive approximation advanced problems George G. Lorentz ; Manfred v. Golitschek ; Yuly Makovoz |
title_fullStr | Constructive approximation advanced problems George G. Lorentz ; Manfred v. Golitschek ; Yuly Makovoz |
title_full_unstemmed | Constructive approximation advanced problems George G. Lorentz ; Manfred v. Golitschek ; Yuly Makovoz |
title_short | Constructive approximation |
title_sort | constructive approximation advanced problems |
title_sub | advanced problems |
topic | Approximation, Théorie de l' Approximation, théorie de l' ram Fourier-analyse gtt approximation Padé inriac approximation avec contrainte inriac approximation polynomiale inriac approximation rationnelle inriac espace fonction inriac fonction spline inriac ondelette orthogonale inriac polynôme Chebyshev inriac polynôme trigonométrique inriac théorie approximation inriac théorème Weierstrass inriac Approximation theory Approximation (DE-588)4002498-2 gnd Approximationstheorie (DE-588)4120913-8 gnd |
topic_facet | Approximation, Théorie de l' Approximation, théorie de l' Fourier-analyse approximation Padé approximation avec contrainte approximation polynomiale approximation rationnelle espace fonction fonction spline ondelette orthogonale polynôme Chebyshev polynôme trigonométrique théorie approximation théorème Weierstrass Approximation theory Approximation Approximationstheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007082899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000000395 |
work_keys_str_mv | AT lorentzgeorgeg constructiveapproximationadvancedproblems AT golitschekmanfredvon constructiveapproximationadvancedproblems AT makovozyuly constructiveapproximationadvancedproblems |