Korovkin type approximation theory and its applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York
de Gruyter
1994
|
| Schriftenreihe: | De Gruyter studies in mathematics
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 627 S. graph. Darst. |
| ISBN: | 3110141787 |
Internformat
MARC
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| 100 | 1 | |a Altomare, Francesco |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Korovkin type approximation theory and its applications |c Francesco Altomare ; Michele Campiti |
| 264 | 1 | |a Berlin ; New York |b de Gruyter |c 1994 | |
| 300 | |a XI, 627 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v 17 | |
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Datensatz im Suchindex
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| adam_text | Contents
Introduction 1
Interdependence of sections 8
Notation 10
Chapter 1. Preliminaries 15
1.1 Topology and analysis 15
1.2 Radon measures 20
* 1.3 Some basic principles of probability theory 37
1.4 Selected topics on locally convex spaces 46
* 1.5 Integral representation theory for convex compact sets 54
* 1.6 C0-Semigroups of operators and abstract Cauchy problems 61
Chapter 2. Korovkin-type theorems for bounded positive Radon measures 74
2.1 Determining subspaces for bounded positive Radon measures 74
2.2 Determining subspaces for discrete Radon measures 87
2.3 Determining subspaces and Chebyshev systems 100
2.4 Convergence subspaces associated with discrete Radon measures 108
2.5 Determining subspaces for Dirac measures 114
2.6 Choquet boundaries 124
Chapter 3. Korovkin-type theorems for positive linear operators 141
3.1 Korovkin closures and Korovkin subspaces for positive linear 141
operators
3.2 Special properties of Korovkin closures 155
3.3 Korovkin subspaces for positive projections 169
3.4 Korovkin subspaces for finitely defined operators 180
Chapter 4. Korovkin-type theorems for the identity operator 195
4.1 Korovkin closures and Korovkin subspaces for the identity 195
operator
4.2 Strict Korovkin subsets. Korovkin s theorems 212
4.3 Korovkin closures and state spaces. Spaces of parabola-like 227
functions
4.4 Korovkin closures and Stone-Weierstrass theorems 237
4.5 Finite Korovkin sets 248
x Contents
Chapter 5. Applications to positive approximation processes on real 264
intervals
5.1 Moduli of continuity and degree of approximation by positive 265
linear operators
5.2 Probabilistic methods and positive approximation processes 283
5.3 Discrete-type approximation processes 320
5.4 Convolution operators and summation processes 352
Chapter 6. Applications to positive approximation processes on 377
convex compact sets
6.1 Positive approximation processes associated with positive 378
projections
6.2 Positive projections and their associated Feller semigroups 423
6.3 Miscellaneous examples and degenerate diffusion equations on 447
convex compact subsets of W
Appendices 481
A. Korovkin-type approximation theory on commutative Banach algebras, 481
by M. Pannenberg
A.I Universal Korovkin-type approximation theory on commutative 483
Banach algebras
A.2 Commutative group algebras 497
A.3 Finitely generated commutative Banach algebras and polydisk 503
algebras
A.4 Generalized analytic functions and algebras generated by inner 510
functions
A. 5 Extreme spectral states and the Gleason-Kahane-Zelazko 513
property
B. Korovkin-type approximation theory on C*-algebras, by F. Beckhoff 518
B.I Approximation by positive linear functional 519
B.2 Approximation by positive linear operators 521
C. A list of determining sets and Korovkin sets 526
C.I Determining sets in ^(X) {X locally compact Hausdorff space) 526
C.2 Determining sets in ^(X) (X compact) 528
C.3 Korovkin sets in ^0(X) (X locally compact Hausdorff space) 530
C.4 Korovkin sets in ^(X) (X compact Hausdorff space) 532
C.5 Korovkin sets in V(X, /*)-spaces 535
Contents xi
D. A subject classification of Korovkin-type approximation theory with a 537
subject index
D.I Subject classification (SC) 538
D.2 Subject index 541
Bibliography 555
Symbol index 607
Subject index 617
|
| adam_txt |
Contents
Introduction 1
Interdependence of sections 8
Notation 10
Chapter 1. Preliminaries 15
1.1 Topology and analysis 15
1.2 Radon measures 20
* 1.3 Some basic principles of probability theory 37
1.4 Selected topics on locally convex spaces 46
* 1.5 Integral representation theory for convex compact sets 54
* 1.6 C0-Semigroups of operators and abstract Cauchy problems 61
Chapter 2. Korovkin-type theorems for bounded positive Radon measures 74
2.1 Determining subspaces for bounded positive Radon measures 74
2.2 Determining subspaces for discrete Radon measures 87
2.3 Determining subspaces and Chebyshev systems 100
2.4 Convergence subspaces associated with discrete Radon measures 108
2.5 Determining subspaces for Dirac measures 114
2.6 Choquet boundaries 124
Chapter 3. Korovkin-type theorems for positive linear operators 141
3.1 Korovkin closures and Korovkin subspaces for positive linear 141
operators
3.2 Special properties of Korovkin closures 155
3.3 Korovkin subspaces for positive projections 169
3.4 Korovkin subspaces for finitely defined operators 180
Chapter 4. Korovkin-type theorems for the identity operator 195
4.1 Korovkin closures and Korovkin subspaces for the identity 195
operator
4.2 Strict Korovkin subsets. Korovkin's theorems 212
4.3 Korovkin closures and state spaces. Spaces of parabola-like 227
functions
4.4 Korovkin closures and Stone-Weierstrass theorems 237
4.5 Finite Korovkin sets 248
x Contents
Chapter 5. Applications to positive approximation processes on real 264
intervals
5.1 Moduli of continuity and degree of approximation by positive 265
linear operators
5.2 Probabilistic methods and positive approximation processes 283
5.3 Discrete-type approximation processes 320
5.4 Convolution operators and summation processes 352
Chapter 6. Applications to positive approximation processes on 377
convex compact sets
6.1 Positive approximation processes associated with positive 378
projections
6.2 Positive projections and their associated Feller semigroups 423
6.3 Miscellaneous examples and degenerate diffusion equations on 447
convex compact subsets of W
Appendices 481
A. Korovkin-type approximation theory on commutative Banach algebras, 481
by M. Pannenberg
A.I Universal Korovkin-type approximation theory on commutative 483
Banach algebras
A.2 Commutative group algebras 497
A.3 Finitely generated commutative Banach algebras and polydisk 503
algebras
A.4 Generalized analytic functions and algebras generated by inner 510
functions
A. 5 Extreme spectral states and the Gleason-Kahane-Zelazko 513
property
B. Korovkin-type approximation theory on C*-algebras, by F. Beckhoff 518
B.I Approximation by positive linear functional 519
B.2 Approximation by positive linear operators 521
C. A list of determining sets and Korovkin sets 526
C.I Determining sets in ^(X) {X locally compact Hausdorff space) 526
C.2 Determining sets in ^(X) (X compact) 528
C.3 Korovkin sets in ^0(X) (X locally compact Hausdorff space) 530
C.4 Korovkin sets in ^(X) (X compact Hausdorff space) 532
C.5 Korovkin sets in V(X, /*)-spaces 535
Contents xi
D. A subject classification of Korovkin-type approximation theory with a 537
subject index
D.I Subject classification (SC) 538
D.2 Subject index 541
Bibliography 555
Symbol index 607
Subject index 617 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:37:50Z |
| indexdate | 2024-07-09T21:24:29Z |
| institution | BVB |
| isbn | 3110141787 |
| language | English |
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| physical | XI, 627 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | de Gruyter |
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| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Altomare, Francesco Verfasser aut Korovkin type approximation theory and its applications Francesco Altomare ; Michele Campiti Berlin ; New York de Gruyter 1994 XI, 627 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 17 Approximation theory Korovkin-Satz (DE-588)4351220-3 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Positiver Operator (DE-588)4046876-8 gnd rswk-swf Approximation (DE-588)4002498-2 s Positiver Operator (DE-588)4046876-8 s Korovkin-Satz (DE-588)4351220-3 s DE-604 Campiti, Michele Verfasser aut De Gruyter studies in mathematics 17 (DE-604)BV000005407 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016875682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Altomare, Francesco Campiti, Michele Korovkin type approximation theory and its applications De Gruyter studies in mathematics Approximation theory Korovkin-Satz (DE-588)4351220-3 gnd Approximation (DE-588)4002498-2 gnd Positiver Operator (DE-588)4046876-8 gnd |
| subject_GND | (DE-588)4351220-3 (DE-588)4002498-2 (DE-588)4046876-8 |
| title | Korovkin type approximation theory and its applications |
| title_auth | Korovkin type approximation theory and its applications |
| title_exact_search | Korovkin type approximation theory and its applications |
| title_exact_search_txtP | Korovkin type approximation theory and its applications |
| title_full | Korovkin type approximation theory and its applications Francesco Altomare ; Michele Campiti |
| title_fullStr | Korovkin type approximation theory and its applications Francesco Altomare ; Michele Campiti |
| title_full_unstemmed | Korovkin type approximation theory and its applications Francesco Altomare ; Michele Campiti |
| title_short | Korovkin type approximation theory and its applications |
| title_sort | korovkin type approximation theory and its applications |
| topic | Approximation theory Korovkin-Satz (DE-588)4351220-3 gnd Approximation (DE-588)4002498-2 gnd Positiver Operator (DE-588)4046876-8 gnd |
| topic_facet | Approximation theory Korovkin-Satz Approximation Positiver Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016875682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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