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1.
We are interested in minimizing functionals with ℓ2 data and gradient fitting term and ℓ1 regularization term with higher order derivatives in a discrete setting. We examine the structure of the solution in 1D by reformulating the original problem into a contact problem which can be solved by dual optimization techniques. The solution turns out to be a ’smooth’ discrete polynomial spline whose knots coincide with the contact points while its counterpart in the contact problem is a discrete version of a spline with higher defect and contact points as knots. In 2D we modify Chambolle’s algorithm to solve the minimization problem with the ℓ1 norm of interacting second order partial derivatives as regularization term. We show that the algorithm can be implemented efficiently by applying the fast cosine transform. We demonstrate by numerical denoising examples that the ℓ2 gradient fitting term can be used to avoid both edge blurring and staircasing effects.   相似文献   

2.
We introduce two new local 1-indices of the same type as the Bourgain 1-index; the +1-index and the +1-weakly null index. We show that the +1-weakly null index of a Banach space X is the same as the Szlenk index of X, provided X does not contain 1. The +1-weakly null index has the same form as the Bourgain 1-index: if it is countable it must take values for some <1. The different 1-indices are closely related and so knowing the Szlenk index of a Banach space helps us calculate its 1-index, via the +1-weakly null index. We show that I(C())=^1++1.  相似文献   

3.
Suppose π1(E, F) is the space of all absolutely 1-summing operators between two Banach spacesE andF. We show that ifF has a copy of c0, then π1 (E, F) will have a copy of c0, and under some conditions ifE has a copy of ℓ1 then π1 (E, F) would have a complemented copy of ℓ1.  相似文献   

4.
For Ω bounded and open subset of andX a reflexive Banach space with 1-symmetric basis, the function spaceJF X (Ω) is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature thatJF X (Ω) does not contain an isomorphic copy of ℓ1. We also investigate the structure of these spaces and their duals.  相似文献   

5.
We give new characterizations of Banach spaces not containing ℓ1 in terms of integral and p-dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.  相似文献   

6.
We obtain a local characterization of the point of continuity property for bounded subsets in Banach spaces not containing basic sequences equivalent to the standard basis of ℓ1 and, as a consequence, we deduce that, in Banach spaces with a separable dual, every closed, bounded, convex and nonempty subset failing the point of continuity property contains a further subset which can be seen inside the set of Borel regular probability measures on the Cantor set in a weak-star dense way. Also, we characterize in terms of trees the point of continuity property of Banach spaces not containing ℓ1, by proving that a Banach space not containing ℓ1 satis- fies the point of continuity property if, and only if, every seminormalized weakly null tree has a boundedly complete branch.  相似文献   

7.
The cell structure of the spaces ℳ2,1 and ℳ3,1 is considered. These are the spaces of complex curves of genus 2 and 3 with one marked point. For the space ℳ2,1, nine cells of the highest dimension 8 are described and their adjacency is studied. For the space ℳ3,1, a list of all 1726 cells of the highest dimension 14 (with orientation) is obtained. The list of adjacent couples of cells is also obtained. These lists can be found on the web.  相似文献   

8.
In this paper, we give some sufficient conditions under which perturbations preserve ? p -localized frames. Using an arbitrary given sequence, we provide a simple way for constructing ? p -localized sequences.  相似文献   

9.
10.
We show that if L is a semilattice then the ℓ1-convolution algebra of L is biflat precisely when L is "uniformly locally finite". Our proof technique shows in passing that if this convolution algebra is biflat then it is isomorphic as a Banach algebra to the Banach space ℓ1(L) equipped with pointwise multiplication. At the end we sketch how these techniques may be extended to prove an analogous characterisation of biflatness for Clifford semigroup algebras.  相似文献   

11.
 For a fixed q  ℕ and a given Σ1 definition φ(d,x), where d is a parameter, we construct a model M of 1 Δ0 + ? exp and a non standard d  M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ(d,x) having no more than q alternations of blocks of quantifiers. Received: 29 September 1998 / Revised version: 7 November 2001 Published online: 10 October 2002 RID="⋆" ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13. RID="⋆" ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13.  相似文献   

12.
We use the Algorithm Z on partitions due to Zeilberger, in a variant form, to give a combinatorial proof of Ramanujan’s 1 ψ 1 summation formula.  相似文献   

13.
The partial ordering of Medvedev reducibility restricted to the family of 01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a 01 class, which we call a ``c.e. separating class'. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes. Mathematics Subject Classification (2000): 03D30, 03D25  相似文献   

14.
We study the restrictions of infinitesimally irreducible modular representations of algebraic groups of type An to subsystem subgroups of type A1 × A1. Under some restrictions on the highest weight of a representation we find their composition factors.  相似文献   

15.
Let w and M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty 10 subsets of 2, under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of w. We show that many countable distributive lattices are lattice-embeddable below any non-zero element of M.Simpsons research was partially supported by NSF Grant DMS-0070718. We thank the anonymous referee for a careful reading of this paper and helpful comments.  相似文献   

16.
This paper presents new results pertaining to the delay-dependent stability and control synthesis of a class of linear switched continuous-time systems with time-varying delays. A new state transformation is introduced to exhibit the delay-dependent dynamics in the slow-time scale. For stability, we construct an appropriate selective Lyapunov functional to derive delay-dependent LMI-based sufficient conditions under arbitrary switching and without relying to overbounding. For the control synthesis, we design switched feedback schemes based on quadratic ℋ2, ℋ and simultaneous ℋ2/ℋ performance criteria. Under the developed transformation, it is established that both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.  相似文献   

17.
We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices.  相似文献   

18.
The existence of p-universal diagonally dominant symmetric liner operators on separable Hilbert spaces is discussed. Also, properties of these operators and their characterization in terms of their spectra are investigated.  相似文献   

19.
One partially ordered set, Q, is a Tukey quotient of another, P, if there is a map ? : PQ carrying cofinal sets of P to cofinal sets of Q. Two partial orders which are mutual Tukey quotients are said to be Tukey equivalent. Let X be a space and denote by \(\mathcal {K}(X)\) the set of compact subsets of X, ordered by inclusion. The principal object of this paper is to analyze the Tukey equivalence classes of \(\mathcal {K}(S)\) corresponding to various subspaces S of ω 1, their Tukey invariants, and hence the Tukey relations between them. It is shown that ω ω is a strict Tukey quotient of \({\Sigma }(\omega ^{\omega _{1}})\) and thus we distinguish between two Tukey classes out of Isbell’s ten partially ordered sets from (Isbell, J. R.: J. London Math Society 4(2), 394–416, 1972). The relationships between Tukey equivalence classes of \(\mathcal {K}(S)\), where S is a subspace of ω 1, and \(\mathcal {K}(M)\), where M is a separable metrizable space, are revealed. Applications are given to function spaces.  相似文献   

20.
Given separable Banach spaces X, Y, Z and a bounded linear operator T:XY, then T is said to preserve a copy of Z provided that there exists a closed linear subspace E of X isomorphic to Z and such that the restriction of T to E is an into isomorphism. It is proved that every operator on C([0,1]) which preserves a copy of an asymptotic ℓ1 space also preserves a copy of C([0,1]).  相似文献   

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