Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group over a nonarchimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands dual group. This was known earlier in the special case where G(K) is an inner form of a split group.

For an edge-bicolored graph G where each edge is colored either red or blue, a vertex set S is a dual feedback vertex set if S hits all blue cycles and red cycles of G. In this paper, we show that a dual feedback vertex set of size at most k can be found in time O∗(ck1) and all minimal dual feedback vertex set of size at most k can be enumerated in time O(c +k 2 ) by compact representations for...

Let {xn} be a frame for a Hilbert space H. We investigate the conditions under which there exists a dual frame for {xn} which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether {xn} can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is ...

In this note, we prove that H is a g-closed subgroup of the compact group K if and only if every sequentially continuous character of the dual of H is continuous-in other words, if the dual of H is a so-called sk-group. We conclude that every countable subgroup of a compact group is g-closed, and thus give a positive answer to a problem of Dikranjan, Milan and Tonolo. We also show that the rela...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the c...

We give a counterexample to the following conjecture of Kauuman 2]: Conjecture Let K be an amphicheiral alternating knot. Then there exists a reduced alternating knot-diagram D of K, such that G(D) is isomorphic to G (D), where G(D) is a checkerboard-graph of D and G (D) its dual.

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

R ring (always commutative and Noetherian) (R,m,k) local ring with maximal ideal m and k = R/m L,M,N, . . . R-modules (always finitely generated) M HomR(M,R), the dual of M D(M) the Auslander dual of M (Definition 2) σM : M wM∗∗ the natural evaluation map; KM = Ker(σM ), CM = Coker(σM ) G-dimR(M),G-dim(M) Gorenstein dimension of M (Definition 16) G-dim(M) <loc ∞ M has locally finite Gorenstein ...