The role of exact fundamental solutions in the study of linear PDEs is illustrated by several examples among equations of mixed type, subelliptic and degenerate elliptic equations, and hyperbolic equations. In particular, we derive exact fundamental solutions for the degenerate hyperbolic operators \( \partial _t^2 - {\partial ^{2l}}\vartriangle \) in \( {{\mathbb{R}}^{{2p}}} \times \mathbb{R} \) for arbitrary1 p =1, 2,….


Fundamental Solution Heat Kernel Heisenberg Group Pseudodifferential Operator Transport Operator 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Richard Beals
    • 1
  1. 1.Department of MathematicsYale UniversityNew Haven

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