Pietro CorvajaDipartimento di Matematica e Informatica, Università di UdineUmberto ZannierScuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa, Italy
Robert BermanDepartment of Mathematics, Chalmers University of TechnologyBo BerndtssonDepartment of Mathematics, Chalmers University of TechnologyJohannes SjöstrandCentre de Mathématiques Laurent Schwartz, Ecole Polytechnique
We give an elementary proof of the existence of an asymptotic expansion in powers of$k$of the Bergman kernel associated to$L$^{$k$}, where$L$is a positive line bundle over a compact complex manifold. We also give an algorithm for computing the coefficients in the expansion.
Let Ω⊂$R$^{$n$}be an arbitrary open set. In this paper it is shown that if a Sobolev function$f$∈$W$^{1,$p$}(Ω) possesses a zero trace (in the sense of Lebesgue points) on ϖΩ, then$f$is weakly zero on ϖΩ in the sense that$f$∈$W$_{0}^{1,$p$}(Ω).
Williams D P. Crossed products of C*-algebras[C]., 2007.
2
Busby R C. DOUBLE CENTRALIZERS AND EXTENSIONS OF C*-ALGEBRAS[J]. Transactions of the American Mathematical Society, 2014, 132(1).
3
Akemann C A, Pedersen G K, Tomiyama J, et al. Multipliers of C∗-algebras[J]. Journal of Functional Analysis, 1973, 13(3): 277-301.
4
Mackey G W. Infinite-dimensional group representations[J]. Bulletin of the American Mathematical Society, 1963, 69(5): 628-686.
5
Ellis R W. Locally compact transformation groups[J]. Duke Mathematical Journal, 1957, 24(2): 119-125.
6
Fell J M. Weak containment and induced representations of groups. II[J]. Transactions of the American Mathematical Society, 1964, 110(3): 424-447.
7
Robert C Busby. Double centralizers and extensions of *-algebras. 1968.
8
Mathai V, Rosenberg J. T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology[J]. Communications in Mathematical Physics, 2004, 253(3): 705-721.
9
Green P. C -ALGEBRAS OF TRANSFORMATION GROUPS WITH SMOOTH ORBIT SPACE[J]. Pacific Journal of Mathematics, 1977, 72(1): 71-97.
10
Karl H Hofmann. Representations of algebras by continuous sections. 1972.