Functional Analytic Methods for Heat Green Operators Heat Kernel Asymptotics via the Weyl-Hörmander Calculus /
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 We...
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| Yhteisötekijä: | |
| Aineistotyyppi: | Elektroninen E-kirja |
| Kieli: | englanti |
| Julkaistu: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Painos: | 1st ed. 2024. |
| Sarja: | Lecture Notes in Mathematics,
2354 |
| Aiheet: | |
| Linkit: | https://doi.org/10.1007/978-3-031-66612-4 |
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Sisällysluettelo:
- - 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.