Language:
English
繁體中文
Help
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
Geometric Approximation Theory
~
Alimov, Alexey R.
Geometric Approximation Theory
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Geometric Approximation Theory/ by Alexey R. Alimov, Igor’ G. Tsar’kov.
Author:
Alimov, Alexey R.
other author:
Tsar’kov, Igor’ G.
Description:
XXI, 508 p. 21 illus.online resource. :
Contained By:
Springer Nature eBook
Subject:
Approximation theory. -
Online resource:
https://doi.org/10.1007/978-3-030-90951-2
ISBN:
9783030909512
Geometric Approximation Theory
Alimov, Alexey R.
Geometric Approximation Theory
[electronic resource] /by Alexey R. Alimov, Igor’ G. Tsar’kov. - 1st ed. 2021. - XXI, 508 p. 21 illus.online resource. - Springer Monographs in Mathematics,2196-9922. - Springer Monographs in Mathematics,.
Main notation, definitions, auxillary results, and examples -- Chebyshev alternation theorem, Haar and Mairhuber's theorems -- Best approximation in Euclidean spaces -- Existence and compactness -- Characterization of best approximation -- Convexity of Chebyshev sets and sums -- Connectedness and stability -- Existence of Chebyshev subspaces -- Efimov–Stechkin spaces. Uniform convexity and uniform smoothness. Uniqueness and strong uniqueness of best approximation in uniformly convex spaces -- Solarity of Chebyshev sets -- Rational approximation -- Haar cones and varisolvencity -- Approximation of vector-valued functions -- The Jung constant -- Chebyshev centre of a set -- Width. Approximation by a family of sets -- Approximative properties of arbitrary sets -- Chebyshev systems of functions in the spaces C, Cn, and Lp -- Radon, Helly, and Carathéodory theorems. Decomposition theorem -- Some open problems -- Index.
This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental results for both these and related problems, many of which appear for the first time in monograph form. The text also discusses the interrelations between main objects of geometric approximation theory, formulating a number of auxiliary problems for demonstration. Central ideas include the problems of existence and uniqueness of elements of best approximations as well as properties of sets including subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a basis for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied viewpoints and especially researchers interested in advanced aspects of the field. .
ISBN: 9783030909512
Standard No.: 10.1007/978-3-030-90951-2doiSubjects--Topical Terms:
527707
Approximation theory.
LC Class. No.: QA221-224
Dewey Class. No.: 511.4
Geometric Approximation Theory
LDR
:03606nam a22004095i 4500
001
1059473
003
DE-He213
005
20220329045051.0
007
cr nn 008mamaa
008
220414s2021 sz | s |||| 0|eng d
020
$a
9783030909512
$9
978-3-030-90951-2
024
7
$a
10.1007/978-3-030-90951-2
$2
doi
035
$a
978-3-030-90951-2
050
4
$a
QA221-224
072
7
$a
PBKJ
$2
bicssc
072
7
$a
MAT034000
$2
bisacsh
072
7
$a
PBKJ
$2
thema
082
0 4
$a
511.4
$2
23
100
1
$a
Alimov, Alexey R.
$e
author.
$0
(orcid)0000-0001-8806-1593
$1
https://orcid.org/0000-0001-8806-1593
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1366178
245
1 0
$a
Geometric Approximation Theory
$h
[electronic resource] /
$c
by Alexey R. Alimov, Igor’ G. Tsar’kov.
250
$a
1st ed. 2021.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2021.
300
$a
XXI, 508 p. 21 illus.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
490
1
$a
Springer Monographs in Mathematics,
$x
2196-9922
505
0
$a
Main notation, definitions, auxillary results, and examples -- Chebyshev alternation theorem, Haar and Mairhuber's theorems -- Best approximation in Euclidean spaces -- Existence and compactness -- Characterization of best approximation -- Convexity of Chebyshev sets and sums -- Connectedness and stability -- Existence of Chebyshev subspaces -- Efimov–Stechkin spaces. Uniform convexity and uniform smoothness. Uniqueness and strong uniqueness of best approximation in uniformly convex spaces -- Solarity of Chebyshev sets -- Rational approximation -- Haar cones and varisolvencity -- Approximation of vector-valued functions -- The Jung constant -- Chebyshev centre of a set -- Width. Approximation by a family of sets -- Approximative properties of arbitrary sets -- Chebyshev systems of functions in the spaces C, Cn, and Lp -- Radon, Helly, and Carathéodory theorems. Decomposition theorem -- Some open problems -- Index.
520
$a
This monograph provides a comprehensive introduction to the classical geometric approximation theory, emphasizing important themes related to the theory including uniqueness, stability, and existence of elements of best approximation. It presents a number of fundamental results for both these and related problems, many of which appear for the first time in monograph form. The text also discusses the interrelations between main objects of geometric approximation theory, formulating a number of auxiliary problems for demonstration. Central ideas include the problems of existence and uniqueness of elements of best approximations as well as properties of sets including subspaces of polynomials and splines, classes of rational functions, and abstract subsets of normed linear spaces. The book begins with a brief introduction to geometric approximation theory, progressing through fundamental classical ideas and results as a basis for various approximation sets, suns, and Chebyshev systems. It concludes with a review of approximation by abstract sets and related problems, presenting novel results throughout the section. This text is suitable for both theoretical and applied viewpoints and especially researchers interested in advanced aspects of the field. .
650
0
$a
Approximation theory.
$3
527707
650
1 4
$a
Approximations and Expansions.
$3
672153
700
1
$a
Tsar’kov, Igor’ G.
$e
author.
$1
https://orcid.org/0000-0002-5943-3711
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1366179
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783030909505
776
0 8
$i
Printed edition:
$z
9783030909529
776
0 8
$i
Printed edition:
$z
9783030909536
830
0
$a
Springer Monographs in Mathematics,
$x
1439-7382
$3
1254272
856
4 0
$u
https://doi.org/10.1007/978-3-030-90951-2
912
$a
ZDB-2-SMA
912
$a
ZDB-2-SXMS
950
$a
Mathematics and Statistics (SpringerNature-11649)
950
$a
Mathematics and Statistics (R0) (SpringerNature-43713)
based on 0 review(s)
Multimedia
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login