國立高雄大學圖資館 |

Language: English

Back

Geometric aspects of functional analysisIsrael Seminar (GAFA) 2020-2022 /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric aspects of functional analysisedited by Ronen Eldan ... [et al.].
Reminder of title:	Israel Seminar (GAFA) 2020-2022 /
other author:	Eldan, Ronen.
Published:	Cham :Springer International Publishing :2023.
Description:	viii, 440 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functional analysis
Online resource:	https://doi.org/10.1007/978-3-031-26300-2
ISBN:	9783031263002$q(electronic bk.)

Geometric aspects of functional analysisIsrael Seminar (GAFA) 2020-2022 /
Geometric aspects of functional analysisIsrael Seminar (GAFA) 2020-2022 /[electronic resource] :edited by Ronen Eldan ... [et al.]. - Cham :Springer International Publishing :2023. - viii, 440 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23271617-9692 ;. - Lecture notes in mathematics ;2035..

This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.

ISBN: 9783031263002$q(electronic bk.)

Standard No.: 10.1007/978-3-031-26300-2doiSubjects--Topical Terms:

254076
Functional analysis

LC Class. No.: QA319 / .G46 2023

Dewey Class. No.: 515.7

Geometric aspects of functional analysisIsrael Seminar (GAFA) 2020-2022 /
LDR:02293nmm a2200325 a 4500 001 651493
003 DE-He213
005 20230930002832.0
006 m d
007 cr nn 008maaau
008 240327s2023 sz s 0 eng d
020 $a 9783031263002$q(electronic bk.)
020 $a 9783031262999$q(paper)
024 7 $a 10.1007/978-3-031-26300-2 $2 doi
035 $a 978-3-031-26300-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA319 $b .G46 2023
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
090 $a QA319 $b .G345 2023
245 1 0 $a Geometric aspects of functional analysis $h [electronic resource] : $b Israel Seminar (GAFA) 2020-2022 / $c edited by Ronen Eldan ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a viii, 440 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2327
520 $a This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
650 0 $a Functional analysis $3 254076
650 0 $a Functional differential equations $x Asymptotic theory $v Congresses. $3 569191
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Convex and Discrete Geometry. $3 277230
650 2 4 $a Probability Theory. $3 913371
700 1 $a Eldan, Ronen. $3 961735
710 2 $a SpringerLink (Online service) $3 273601
711 2 $n (3rd : $d 1998 : $c Amsterdam, Netherlands) $3 194767
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-26300-2
950 $a Mathematics and Statistics (SpringerNature-11649)