User:Holmansf/Egorov's theorem (pseudodifferential operators)

In the theory of pseudodifferential operators (ψDOs), an area of mathematics, Egorov's Theorem shows that when a ψDO is conjugated by Fourier integral operators, the result is again a ψDO. Furthermore, the theorem gives a simple formula for the principal symbol of the resulting ψDO. The theorem is named after Yurii Vladimirovich Egorov (see here for a brief profile) who first proved the result in (Egorov 1969). The theorem is a major ingredient in the parametrix construction and resulting existence results for general partial differential equations of principal type.

Bibliography

• Egorov, Yu. V. (1969), "The canonical transformations of pseudodifferential operators", Uspekhi Matematicheskikh Nauk (in Russian), 24 (5(149)): 235–236, MR 0265748, Zbl 0191.43802 {{citation}}: Cite has empty unknown parameter: |month= (help).