H functional calculus for an elliptic operator on a half-space with general boundary conditions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 3, pp. 487-543.

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

Classification : 47A60, 35J40, 47F05
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Dore, Giovanni; Venni, Alberto. $H^\infty $ functional calculus for an elliptic operator on a half-space with general boundary conditions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 3, pp. 487-543. http://www.numdam.org/item/ASNSP_2002_5_1_3_487_0/

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