共查询到20条相似文献,搜索用时 31 毫秒
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Bent Ørsted 《Journal of Functional Analysis》1979,31(3):355-359
We present a brief and elementary proof of the Imprimitivity Theorem for an arbitrary locally compact group. 相似文献
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《Quaestiones Mathematicae》2013,36(1-3):67-71
Abstract Let K: P → T be a fixed functor. A criterion is given for a functor M': T → V to be a (right) Kan extension along K of some functor M: P → V. The functors M having a given M' as Kan extension are, in general, classified by continuous functors (V P)o → V. We introduce a notion of system of imprimitivity, generalizing that of Mackey; when the shape category of K is codense in the systems of imprimitivity classify the functors H having M' as Kan extension. As a special case one obtains Mackey's Imprimitivity Theorem for finite groups. 相似文献
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Induced representations of *-algebras by unbounded operators in Hilbert space are investigated. Conditional expectations of a *-algebra ${{\mathcal{A}}}$ onto a unital *-subalgebra ${{\mathcal{B}}}$ are introduced and used to define inner products on the corresponding induced modules. The main part of the paper is concerned with group graded *-algebras ${{\mathcal{A}}}=\oplus_{g\in G}{{\mathcal{A}}}_g$ for which the *-subalgebra ${{\mathcal{B}}}:={{\mathcal{A}}}_e$ is commutative. Then the canonical projection $p:{{\mathcal{A}}}\to{{\mathcal{B}}}$ is a conditional expectation and there is a partial action of the group G on the set ${{\mathcal{B}}}p$ of all characters of ${{\mathcal{B}}}$ which are nonnegative on the cone $\sum{{\mathcal{A}}}^2{{\mathcal{A}}}p{{\mathcal{B}}}.$ The complete Mackey theory is developed for *-representations of ${{\mathcal{A}}}$ which are induced from characters of ${{\widehat{{{\mathcal{B}}}}^+}}.$ Systems of imprimitivity are defined and two versions of the Imprimitivity Theorem are proved in this context. A concept of well-behaved *-representations of such *-algebras ${{\mathcal{A}}}$ is introduced and studied. It is shown that well-behaved representations are direct sums of cyclic well-behaved representations and that induced representations of well-behaved representations are again well-behaved. The theory applies to a large variety of examples. For important examples such as the Weyl algebra, enveloping algebras of the Lie algebras su(2), su(1,1), and of the Virasoro algebra, and *-algebras generated by dynamical systems our theory is carried out in great detail. 相似文献
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Ming-Chien Yang 《Applied mathematics and computation》2010,216(12):3754-3760
The n-dimensional star graph Sn is an attractive alternative to the hypercube graph and is a bipartite graph with two partite sets of equal size. Let Fv and Fe be the sets of faulty vertices and faulty edges of Sn, respectively. We prove that Sn − Fv − Fe contains a fault-free cycle of every even length from 6 to n! − 2∣Fv∣ with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. We also show that Sn − Fv − Fe contains a fault-free path of length n! − 2∣Fv∣ − 1 (respectively, n! − 2∣Fv∣ − 2) between two arbitrary vertices of Sn in different partite sets (respectively, the same partite set) with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. 相似文献
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Joachim Toft 《Applied and Computational Harmonic Analysis》2019,46(1):154-176
We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator is a Schatten-q operator from to and r-nuclear operator from to when for suitable p, q and r in . 相似文献
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《Discrete Mathematics》2020,343(3):111721
The -additive codes are subgroups of , and can be seen as a generalization of linear codes over and . A -linear Hadamard code is a binary Hadamard code which is the Gray map image of a -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some -linear Hadamard codes of length are equivalent, once is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to , this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on , the full classification of the -linear Hadamard codes of length is established by giving the exact number of such codes. 相似文献
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A compact graph-like space is a triple , where is a compact, metrizable space, is a closed zero-dimensional subset, and is an index set such that . New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta. 相似文献
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The bounded edge-connectivity λk(G) of a connected graph G with respect to is the minimum number of edges in G whose deletion from G results in a subgraph with diameter larger than k and the edge-persistence D+(G) is defined as λd(G)(G), where d(G) is the diameter of G. This paper considers the Cartesian product G1×G2, shows λk1+k2(G1×G2)≥λk1(G1)+λk2(G2) for k1≥2 and k2≥2, and determines the exact values of D+(G) for G=Cn×Pm, Cn×Cm, Qn×Pm and Qn×Cm. 相似文献
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