Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians. III
type: Item
instance of: scholarly article
title: Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians. III
zbMATH Open document ID: 0886.35003
author: Bernard Gaveau
author: Peter C. Greiner
author: Richard Beals
published in: Bulletin des Sciences Mathématiques
publication date: 1998-05-10T00:00:00Z
review text: This last part (III) concerns the construction of a parametrix for \(\Delta_X\) starting with the case when \(X_j\); \(j=1,\dots,2n\) are real-analytic coefficients. In this case the authors consider also the modified operator \(\Delta= \Delta_X\) plus lower order terms \(\Delta_0, \Delta_1\) and for systems with appropriately modified \(v_k\)s and \(w_k\)s. For the general case when the \(X_j\) are only \(C^\infty\) coefficients when one cannot construct a Hamiltonian path, an analytic approximation is considered for \(X_j\) and, corresponding to this approximation, one obtains approximate solutions for the Hamilton-Jacobi equations and for the transport equations. Finally, one proves that a similar expression of the parametrix, as that in the case when the \(X_j\) are real analytic coefficients, holds also in the general case.
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70H20
zbMATH DE Number: 1019541
zbMATH Keywords: analytic approximation
zbMATH Keywords: transport equations
MaRDI profile type: Publication
Recommended article: Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians. I
Recommended article: Complex Hamiltonian mechanics and parametrices for subelliptic Laplacians. II
Recommended article: Real and complex Hamiltonian mechanics on some sub-Riemannian manifolds
Recommended article: Q5474592
Recommended article: THE COMPLEXITY OF INTEGRABLE HAMILTONIAN SYSTEMS ON A PRESCRIBED THREE-DIMENSIONAL CONSTANT-ENERGY SUBMANIFOLD
Recommended article: Q3362738
Recommended article: Q5424782
Recommended article: Complex calculus of variations and explicit solutions for complex Hamilton-Jacobi equations
Recommended article: Hamiltonian-minimal Lagrangian submanifolds in complex space forms
Recommended article: Hamiltonian systems on complex Grassmann manifolds. Holonomy and Schrödinger equation
description: scientific article; zbMATH DE number 1019541