共查询到4条相似文献,搜索用时 0 毫秒
1.
Pablo Ramacher 《Journal of Functional Analysis》2008,255(4):777-818
Let G⊂O(n) be a compact group of isometries acting on n-dimensional Euclidean space Rn, and X a bounded domain in Rn which is transformed into itself under the action of G. Consider a symmetric, classical pseudodifferential operator A0 in L2(Rn) with G-invariant Weyl symbol, and assume that it is semi-bounded from below. We show that the spectrum of the Friedrichs extension A of the operator is discrete, and derive asymptotics for the number Nχ(λ) of eigenvalues of A less or equal λ and with eigenfunctions in the χ-isotypic component of L2(X) as λ→∞, giving also an estimate for the remainder term in case that G is a finite group. In particular, we show that the multiplicity of each unitary irreducible representation in L2(X) is asymptotically proportional to its dimension. 相似文献
2.
We use the characterizations of the classes of all infinite matrices that map the spaces of sequences which are strongly summable or bounded by the Cesàro method of order 1 into the spaces of null or convergent sequences given by Ba?ar, Malkowsky and Altay [Matrix transformations on the matrix domains of triangles in the spaces of strongly C1-summable and bounded sequences, Publ. Math. Debrecen 73 (1-2) (2008), 193-213] and the Hausdorff measure of noncompactness to characterize the classes of all compact operators between those spaces. 相似文献
3.
Ivana Djolovi? Eberhard Malkowsky 《Journal of Mathematical Analysis and Applications》2008,340(1):291-303
We establish some identities or estimates for the operator norms and Hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary BK spaces with AK, or in the spaces of all convergent or bounded sequences, into the spaces of all null, convergent or bounded sequences, or of all absolutely convergent series. Furthermore, we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces, and on the sequence spaces studied in [I. Djolovi?, Compact operators on the spaces and , J. Math. Anal. Appl. 318 (2) (2006) 658-666; I. Djolovi?, On the space of bounded Euler difference sequences and some classes of compact operators, Appl. Math. Comput. 182 (2) (2006) 1803-1811]. 相似文献
4.
Hongzhi HUANG 《Frontiers of Mathematics in China》2020,15(1):69-89
In the study of the collapsed manifolds with bounded sectional curvature,the following two results provide basic tools:a(singular)fibration theorem by K.Fukaya[J.Differential Gcom.,1987.25(1):139156]and J.Cheeger,K.Fukaya,and M.Gromov[J.Airier.Math.Soc.,1992.5(2):327372],and the stability for isometric compact Lie group actions on manifolds by R.S.Palais[Bull.Amer.Math.Soc.,1961,67(4):362364]and K.Grove and H.Karcher[Math.Z..1973,132:1120].The main results in this paper(partially)generalize the two results to manifolds with local bounded Ricci covering geometry. 相似文献