caa a22 4500 465825427 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112296 doi (NATIONALLICENCE)springer-10.1007/BF02112296 Tervo J. University of Kuopio, SF-70211, Kuopio, Finland aut On realizations related to Weyl operators [Elektronische Daten] [J. Tervo] Summary: The paper deals with the minimal and the maximal realizations (L w )~ and (L w )′•:L 2→L 2 of linear operators of Weyl type (1) $$(L{}^w(x,D)\varphi )(x) = (2\pi )^{ - n} \int_{\mathbb{R}^n } {\left( {\int_{\mathbb{R}^n } {L((x + y)/2,\xi )\varphi (y)e^{i< x - y,\xi > } dy} } \right)d\xi }$$ Applying the Weyl symbolic calculus, one establishes sufficient criteria for the equality (L w )~ = (L w )′#, that is, for the essential maximality ofL w (x, D) inL 2. Moreover criteria are obtained for the bijectivity of (L w )~ + CI for large enoughC. When the underlying Riemannian metricg satisfies the conditiong (x,ξ) (y, η) = g (x,ξ) (y, − η), then the operators (1) are related to the pseudo-differential operators (2) $$(L(x,D)\varphi )(x) = (2\pi )^{ - n} \int_{\mathbb{R}^n } {L(x,\xi )(F\varphi )(\xi )e^{i< \xi ,x > } d\xi }$$ throughL(x, D) = A w (x, D), whereA(x, ξ) = e −i〈D x ,D ξ 〉/2 L(x, ξ). From this relation some properties ofL w (x, D) are carried over toL(x, D). For example, criteria forL ~ =L′# are verified. Birkhäuser Verlag, 1990 Primary 35S05 nationallicence Secondary 35A35, 35A05 nationallicence aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 201-234 0001-9054 40:1<201 1990 40 10 https://doi.org/10.1007/BF02112296 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112296 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tervo J. University of Kuopio, SF-70211, Kuopio, Finland aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 201-234 0001-9054 40:1<201 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer