國立高雄大學圖資館 |

Language: English

Back

Functional analytic methods for heat Green operatorsheat kernel asymptotics via the Weyl-Hörmander calculus /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Functional analytic methods for heat Green operatorsby Kazuaki Taira.
Reminder of title:	heat kernel asymptotics via the Weyl-Hörmander calculus /
Author:	Taira, Kazuaki.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xviii, 644 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functional analysis.
Online resource:	https://doi.org/10.1007/978-3-031-66612-4
ISBN:	9783031666124$q(electronic bk.)

Functional analytic methods for heat Green operatorsheat kernel asymptotics via the Weyl-Hörmander calculus /
Taira, Kazuaki.

Functional analytic methods for heat Green operatorsheat kernel asymptotics via the Weyl-Hörmander calculus /[electronic resource] :by Kazuaki Taira. - Cham :Springer Nature Switzerland :2024. - xviii, 644 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23541617-9692 ;. - Lecture notes in mathematics ;2035..

- Introduction and Main Results -- Part I Functional Analytic Approach to Heat Operators -- Preliminaries from Manifold Theory -- Finite Double-Norm and Trace-Class Operators on a Hilbert Space -- Hilbert-Schmidt and Trace-Class Operators on a Manifold -- Analytic Semigroups via Dunford Integrals -- Part II Pseudo-Differential Operators and Elliptic Boundary Value Problems -- Lp Theory of Pseudo-Differential Operators -- Elliptic Boundary Value Problems on a Manifold -- Lp Theory of Elliptic Boundary Value Problems -- Boutet de Monvel Calculus -- Pseudo-Differential Operator Approach to Agmon's Method -- Part III Analytic Semigroup Approach to Heat Operators -- Generation Theorem for Analytic Semigroups via Agmon's Method -- Hypoelliptic Robin Problems via Boutet de Monvel Calculus -- Distribution Kernel of Analytic Semigroups in the Hypoelliptic Case -- Part IV The Fundamental Solution for the Cauchy Problem -- The Cauchy Problem for the Heat Operator on Rn -- Fundamental Solution Operator for the Cauchy Problem on a Manifold -- Part V Symbolic Calculus for Dirichlet, Neumann and Regular Robin Problems -- Symbolic Calculus near the Boundary -- Analytic Version of Weyl Bases for the Heat Kernel on the Half Axis -- Symbolic Calculus for Boundary Value Problems on a Manifold -- Part VI Transport Equations and Trace Formulas on the Half Space -- Transport Equations via the Weyl-Hörmander Calculus -- Several Trace Formulas for Auxiliary Operators on the Half Space -- Part VII Heat Kernel Asymptotics for Dirichlet, Neumann and Regular Robin Problems -- Heat Kernel Asymptotics for the Dirichlet Problem -- Heat Kernel Asymptotics for the Neumann Problem -- Heat Kernel Asymptotics for the Regular Robin Problem -- Heat Kernel Asymptotics for the Generalized Regular Robin Problem -- Part VIII Heat Kernel Asymptotics for the Hypoelliptic Robin Problem -- Heat Kernel Asymptotics for the Hypoelliptic Robin Problem -- Examples in the Plane R2 -- Concluding Remarks.

This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl-Hörmander calculus of pseudo-differential operators to study heat Green operators through concrete calculations for the Dirichlet, Neumann, regular Robin and hypoelliptic Robin boundary conditions. Further, it provides detailed coverage of important examples and applications in elliptic and parabolic problems, illustrated with many figures and tables. A unified mathematical treatment for solving initial boundary value problems for the heat equation under general Robin boundary conditions is desirable, and leads to an extensive study of various aspects of elliptic and parabolic partial differential equations. The principal ideas are explicitly presented so that a broad spectrum of readers can easily understand the problem and the main results. The book will be of interest to readers looking for a functional analytic introduction to the meeting point of partial differential equations, differential geometry and probability.

ISBN: 9783031666124$q(electronic bk.)

Standard No.: 10.1007/978-3-031-66612-4doiSubjects--Topical Terms:

200585
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Functional analytic methods for heat Green operatorsheat kernel asymptotics via the Weyl-Hörmander calculus /
LDR:04324nmm a2200337 a 4500 001 669615
003 DE-He213
005 20240918130251.0
006 m d
007 cr nn 008maaau
008 250120s2024 sz s 0 eng d
020 $a 9783031666124$q(electronic bk.)
020 $a 9783031666117$q(paper)
024 7 $a 10.1007/978-3-031-66612-4 $2 doi
035 $a 978-3-031-66612-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA320
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 QA320 $b .T134 2024
100 1 $a Taira, Kazuaki. $3 357439
245 1 0 $a Functional analytic methods for heat Green operators $h [electronic resource] : $b heat kernel asymptotics via the Weyl-Hörmander calculus / $c by Kazuaki Taira.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xviii, 644 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2354
505 0 $a - Introduction and Main Results -- Part I Functional Analytic Approach to Heat Operators -- Preliminaries from Manifold Theory -- Finite Double-Norm and Trace-Class Operators on a Hilbert Space -- Hilbert-Schmidt and Trace-Class Operators on a Manifold -- Analytic Semigroups via Dunford Integrals -- Part II Pseudo-Differential Operators and Elliptic Boundary Value Problems -- Lp Theory of Pseudo-Differential Operators -- Elliptic Boundary Value Problems on a Manifold -- Lp Theory of Elliptic Boundary Value Problems -- Boutet de Monvel Calculus -- Pseudo-Differential Operator Approach to Agmon's Method -- Part III Analytic Semigroup Approach to Heat Operators -- Generation Theorem for Analytic Semigroups via Agmon's Method -- Hypoelliptic Robin Problems via Boutet de Monvel Calculus -- Distribution Kernel of Analytic Semigroups in the Hypoelliptic Case -- Part IV The Fundamental Solution for the Cauchy Problem -- The Cauchy Problem for the Heat Operator on Rn -- Fundamental Solution Operator for the Cauchy Problem on a Manifold -- Part V Symbolic Calculus for Dirichlet, Neumann and Regular Robin Problems -- Symbolic Calculus near the Boundary -- Analytic Version of Weyl Bases for the Heat Kernel on the Half Axis -- Symbolic Calculus for Boundary Value Problems on a Manifold -- Part VI Transport Equations and Trace Formulas on the Half Space -- Transport Equations via the Weyl-Hörmander Calculus -- Several Trace Formulas for Auxiliary Operators on the Half Space -- Part VII Heat Kernel Asymptotics for Dirichlet, Neumann and Regular Robin Problems -- Heat Kernel Asymptotics for the Dirichlet Problem -- Heat Kernel Asymptotics for the Neumann Problem -- Heat Kernel Asymptotics for the Regular Robin Problem -- Heat Kernel Asymptotics for the Generalized Regular Robin Problem -- Part VIII Heat Kernel Asymptotics for the Hypoelliptic Robin Problem -- Heat Kernel Asymptotics for the Hypoelliptic Robin Problem -- Examples in the Plane R2 -- Concluding Remarks.
520 $a This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl-Hörmander calculus of pseudo-differential operators to study heat Green operators through concrete calculations for the Dirichlet, Neumann, regular Robin and hypoelliptic Robin boundary conditions. Further, it provides detailed coverage of important examples and applications in elliptic and parabolic problems, illustrated with many figures and tables. A unified mathematical treatment for solving initial boundary value problems for the heat equation under general Robin boundary conditions is desirable, and leads to an extensive study of various aspects of elliptic and parabolic partial differential equations. The principal ideas are explicitly presented so that a broad spectrum of readers can easily understand the problem and the main results. The book will be of interest to readers looking for a functional analytic introduction to the meeting point of partial differential equations, differential geometry and probability.
650 0 $a Functional analysis. $3 200585
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Differential Equations. $3 285983
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-66612-4
950 $a Mathematics and Statistics (SpringerNature-11649)