Summary
The hyperbolic symmetrizer is a matrix which symmetrizes in a standard way any Sylvester hyperbolic matrix. This paper deals with the theory of the hyperbolic symmetrizer, its relationships with the concept of Bezout matrix, its perturbations which originate the so–called quasi-symmetrizer and its applications to Cauchy problems for linear weakly hyperbolic equations.
2000 AMS Subject Classification: Primary: 35L30, 35L80; Secondary: 15A21.
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Acknowledgments
The author wishes to thank Peter W. Michor for some useful discussions about Bezout matrix and roots of polynomials, and Armin Rainer, who pointed out, in a private communication, some very interesting links among various types of symmetrizers and the so–called Bezoutiant (for a definition, see for instance [10]).
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Jannelli, E. (2009). The Hyperbolic Symmetrizer: Theory and Applications. In: Bove, A., Del Santo, D., Murthy, M. (eds) Advances in Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 78. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4861-9_7
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DOI: https://doi.org/10.1007/978-0-8176-4861-9_7
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