A note on reduced forms of effectively hyperbolic operators and energy integrals
type: Item
instance of: scholarly article
title: A note on reduced forms of effectively hyperbolic operators and energy integrals
zbMATH Open document ID: 0564.35068
author: Tatsuo Nishitani
published in: Osaka Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Consider a hyperbolic operator with principal symbol P. At a double characteristic point, the coefficient matrix of the Hamiltonian system associated with the quadratic form leading the Taylor expansion in the cotangent bundle is called the fundamental matrix. If the eigenvalues of the matrix are non-zero and real, then the operator is called effectively hyperbolic. The author presents a method, using certain homogeneous canonical transformations, of reducing effectively hyperbolic operators to certain standard forms. He works out some examples which show connections with energy integrals. However the energy integral estimates appear elsewhere.
reviewed by: Steven G. Krantz
Mathematics Subject Classification ID: 35L25
Mathematics Subject Classification ID: 35L40
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 3899428
zbMATH Keywords: double characteristic
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: fundamental matrix
zbMATH Keywords: effectively hyperbolic
zbMATH Keywords: canonical transformations
zbMATH Keywords: standard forms
zbMATH Keywords: energy integrals
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3899428