Displaying similar documents to “On spectral projections of elliptic operators”

Matrix triangulation of hypoelliptic boundary value problems

R. A. Artino, J. Barros-Neto (1992)

Annales de l'institut Fourier

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Given a hypoelliptic boundary value problem on ω × [ 0 , T ) with ω an open set in R n , ( n > 1 ) , we show by matrix triangulation how to reduce it to two uncoupled first order systems, and how to estimate the eigenvalues of the corresponding matrices. Parametrices for the first order systems are constructed. We then characterize hypoellipticity up to the boundary in terms of the Calderon operator corresponding to the boundary value problem.

H ∞ functional calculus for an elliptic operator on a half-space with general boundary conditions

Giovanni Dore, Alberto Venni (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let A be the L p realization ( 1 < p < ∞ ) of a differential operator P ( D x , D t ) on ℝ n × ℝ + with general boundary conditions B k ( D x , D t ) u ( x , 0 ) = 0 ( 1 ≤ k ≤ m ). Here P is a homogeneous polynomial of order 2 m in n + 1 complex variables that satisfies a suitable ellipticity condition, and for 1 ≤ k ≤ m B k is a homogeneous polynomial of order m k < 2 m ; it is assumed that the usual complementing condition is satisfied. We prove that A is a sectorial operator with a bounded H ∞ functional calculus.