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Analysis on manifolds with singularities

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analysis on manifolds with singularitiesby Der-Chen Chang, Bert-Wolfgang Schulze.
作者:	Chang, Der-chen E.
其他作者:	Schulze, Bert-Wolfgang.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	x, 135 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Pseudodifferential operators.
電子資源:	https://doi.org/10.1007/978-3-032-01890-8
ISBN:	9783032018908$q(electronic bk.)

Analysis on manifolds with singularities
Chang, Der-chen E.

Analysis on manifolds with singularities[electronic resource] /by Der-Chen Chang, Bert-Wolfgang Schulze. - Cham :Springer Nature Switzerland :2025. - x, 135 p. :ill. (some col.), digital ;24 cm. - Pseudo-differential operators, theory and applications,v. 162297-0363 ;. - Pseudo-differential operators, theory and applications ;v.11..

Introduction -- 1. Pseudo-differential operators - basics and new techniques -- 1.1. Elements of the local calculus -- 1.2. Operators on manifolds -- 1.3. Twisted symbolic estimates -- 1.4. Edge Sobolev spaces -- 1.5. Explicit solutions to Dirichlet and Neumann problems -- 1.6. Hölder and Lp estimates for coercive boundary value problems -- 2. Operators of Fuchs Type -- 2.1. Degenerate Operators and Singular Manifolds -- 2.2. Kernel Cut-Off -- 2.3. Symbols with Distributional Asymptotic Densities -- 2.4. Conical singularities in stretched descripion -- 2.5. The cone calculus -- 3. Manifolds with edges -- 3.1. Manifolds with edge and weighted Sobolev spaces -- 3.2. Edge spaces with asymptotics -- 3.3. Edge operators -- 4. Edge Operators with Trace and Potential Conditions -- 4.1. Basic Tools -- 4.2. Group Actions and Weighted Cone and Edge Spaces -- 4.3. Operators in Edge Spaces -- 4.4. Notes on Pseudo-Differential Boundary Problems -- 4.5. The Laplace-Beltrami Operator on a Wedge -- 4.6. The Global Ellipticity of Edge Problems -- 4.7. Local Calculus Close to the Edge -- 4.8. Global Ellipticity with Edge Conditions -- 5. The Geometry of Singularities -- 5.1. The Case of Conical Singularities or Edges -- 5.2. Higher Singularities -- 5.3. Iterated Edge Spaces -- 5.4. Distribution spaces and cone operators -- Bibliography.

This exposition introduces new developments of pseudo-differential operators on manifolds with singularities such as conical points, edges, or higher corners, and recent results in these fields. It presents some crucial parts of recent inventions in singular analysis which contribute to pseudo-differential structures and establishes new insight to building up singular operators in corresponding operator algebras with symbolic structures. Researchers in the field will find the presented techniques in this book a valuable resource and inspiration for their own projects.

ISBN: 9783032018908$q(electronic bk.)

Standard No.: 10.1007/978-3-032-01890-8doiSubjects--Topical Terms:

247427
Pseudodifferential operators.

LC Class. No.: QA329.7

Dewey Class. No.: 515.7242

Analysis on manifolds with singularities
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505 0 $a Introduction -- 1. Pseudo-differential operators - basics and new techniques -- 1.1. Elements of the local calculus -- 1.2. Operators on manifolds -- 1.3. Twisted symbolic estimates -- 1.4. Edge Sobolev spaces -- 1.5. Explicit solutions to Dirichlet and Neumann problems -- 1.6. Hölder and Lp estimates for coercive boundary value problems -- 2. Operators of Fuchs Type -- 2.1. Degenerate Operators and Singular Manifolds -- 2.2. Kernel Cut-Off -- 2.3. Symbols with Distributional Asymptotic Densities -- 2.4. Conical singularities in stretched descripion -- 2.5. The cone calculus -- 3. Manifolds with edges -- 3.1. Manifolds with edge and weighted Sobolev spaces -- 3.2. Edge spaces with asymptotics -- 3.3. Edge operators -- 4. Edge Operators with Trace and Potential Conditions -- 4.1. Basic Tools -- 4.2. Group Actions and Weighted Cone and Edge Spaces -- 4.3. Operators in Edge Spaces -- 4.4. Notes on Pseudo-Differential Boundary Problems -- 4.5. The Laplace-Beltrami Operator on a Wedge -- 4.6. The Global Ellipticity of Edge Problems -- 4.7. Local Calculus Close to the Edge -- 4.8. Global Ellipticity with Edge Conditions -- 5. The Geometry of Singularities -- 5.1. The Case of Conical Singularities or Edges -- 5.2. Higher Singularities -- 5.3. Iterated Edge Spaces -- 5.4. Distribution spaces and cone operators -- Bibliography.
520 $a This exposition introduces new developments of pseudo-differential operators on manifolds with singularities such as conical points, edges, or higher corners, and recent results in these fields. It presents some crucial parts of recent inventions in singular analysis which contribute to pseudo-differential structures and establishes new insight to building up singular operators in corresponding operator algebras with symbolic structures. Researchers in the field will find the presented techniques in this book a valuable resource and inspiration for their own projects.
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