Displaying similar documents to “Lecture notes : Spectral properties of non-self-adjoint operators”

The proof of the Nirenberg-Treves conjecture

Nils Dencker (2003)

Journées équations aux dérivées partielles

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We prove the Nirenberg-Treves conjecture : that for principal type pseudo-differential operators local solvability is equivalent to condition ( Ψ ). This condition rules out certain sign changes of the imaginary part of the principal symbol along the bicharacteristics of the real part. We obtain local solvability by proving a localizable estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new metric in the Weyl (or Beals-Fefferman)...

Equiconvergence theorems for Laguerre series

Georgi Karadzhov (1992)

Banach Center Publications

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The Szegö equiconvergence theorem for the Laguerre series is improved. In particular, a system of exact sufficient conditions is given.