國立虎尾科技大學 |

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations/ by Johannes Sjöstrand.
Author:	Sjöstrand, Johannes.
Description:	X, 496 p. 71 illus., 69 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Several Complex Variables and Analytic Spaces. -
Online resource:	https://doi.org/10.1007/978-3-030-10819-9
ISBN:	9783030108199

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Sjöstrand, Johannes.

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations[electronic resource] /by Johannes Sjöstrand. - 1st ed. 2019. - X, 496 p. 71 illus., 69 illus. in color.online resource. - Pseudo-Differential Operators, Theory and Applications,142297-0355 ;. - Pseudo-Differential Operators, Theory and Applications,11.

The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.

ISBN: 9783030108199

Standard No.: 10.1007/978-3-030-10819-9doiSubjects--Topical Terms:

672032
Several Complex Variables and Analytic Spaces.

LC Class. No.: QA331-355

Dewey Class. No.: 515.9

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
LDR:02474nam a22003855i 4500 001 1005147
003 DE-He213
005 20200701042303.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783030108199 $9 978-3-030-10819-9
024 7 $a 10.1007/978-3-030-10819-9 $2 doi
035 $a 978-3-030-10819-9
050 4 $a QA331-355
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515.9 $2 23
100 1 $a Sjöstrand, Johannes. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1298627
245 1 0 $a Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations $h [electronic resource] / $c by Johannes Sjöstrand.
250 $a 1st ed. 2019.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2019.
300 $a X, 496 p. 71 illus., 69 illus. in color. $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 Pseudo-Differential Operators, Theory and Applications, $x 2297-0355 ; $v 14
520 $a The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 0 $a Functions of complex variables. $3 528649
650 0 $a Differential equations. $3 527664
650 0 $a Partial differential equations. $3 1102982
650 0 $a Operator theory. $3 527910
650 1 4 $a Functions of a Complex Variable. $3 672126
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Operator Theory. $3 672127
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030108182
776 0 8 $i Printed edition: $z 9783030108205
830 0 $a Pseudo-Differential Operators, Theory and Applications, $x 2297-0355 ; $v 11 $3 1266177
856 4 0 $u https://doi.org/10.1007/978-3-030-10819-9
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)