共查询到20条相似文献,搜索用时 46 毫秒
1.
Fiedler and Pták called a cone minimal if it is n-dimensional and has n+1 extremal rays. We call a cone almost minimal if it is n-dimensional and has n+2 extremal rays. Duality properties stemming from the use of Gale pairs lead to a general technique for identifying the extreme cone-preserving (positive) operators between polyhedral cones. This technique is most effective for cones with dimension not much smaller than the number of their extreme rays. In particular, the Fiedler-Pták characterization of extreme positive operators between minimal cones is extended to the following cases: (i) operators from a minimal cone to an arbitrary polyhedral cone, (ii) operators from an almost minimal cone to a minimal cone. 相似文献
2.
Juan B. Gil Thomas Krainer Gerardo A. Mendoza 《Journal of Mathematical Analysis and Applications》2008,340(2):1296-1311
We give a simple, explicit, sufficient condition for the existence of a sector of minimal growth for second-order regular singular differential operators on graphs. We specifically consider operators with a singular potential of Coulomb type and base our analysis on the theory of elliptic cone operators. 相似文献
3.
Peter Constantin 《Journal of Functional Analysis》1981,44(1):87-119
Schrödinger operators in a class of domains with asymptotic cones are considered. A generalized Fourier transform representing the absolutely continuous part of the Schrödinger operator as multiplication by in the asymptotic cone is constructed. Wave operators relating the free Laplacian to Schrödinger operators are computed using the generalized Fourier transform. The wave operators relating Schrödinger operators acting in domains with the same asymptotic cone are computed and shown to be complete. 相似文献
4.
John E. Gilbert Andrea R. Nahmod 《Transactions of the American Mathematical Society》1999,351(8):3267-3300
The study of bilinear operators associated to a class of non-smooth symbols can be reduced to ther study of certain special bilinear cone operators to which a time frequency analysis using smooth wave-packets is performed. In this paper we prove that when smooth wave-packets are replaced by Walsh wave-packets the corresponding discrete Walsh model for the cone operators is not only -bounded, as Thiele has shown in his thesis for the Walsh model corresponding to the bilinear Hilbert transform, but actually improves regularity as it maps into a Hardy space. The same result is expected to hold for the special bilinear cone operators.
5.
《Quaestiones Mathematicae》2013,36(1):5-26
Abstract Operators T which are both majorizing and cone absolutely summing on a Banach lattice E are investigated. Compactness and nuclearity of such operators are discussed and it is shown that a trace can be defined for operators belonging to a large class of these operators. Special results are derived in the case where E is a Banach function space and T a kernel operator. Finally we derive strongly measurable representations for a certain class of cone absolutely summing operators thereby clarifying work done by Dinculeanu and J.J. Uhl. 相似文献
6.
7.
Boundary value problems for pseudodifferential operators (with orwithout the transmission property) are characterised as a substructureof the edge pseudodifferential calculus with constant discreteasymptotics. The boundary in this case is the edge and the inner normalthe model cone of local wedges. Elliptic boundary value problems fornoninteger powers of the Laplace symbol belong to the examples as wellas problems for the identity operator in the interior with a prescribednumber of trace and potential conditions. Transmission operators arecharacterised as smoothing Mellin and Green operators with meromorphicsymbols. 相似文献
8.
?ukasz Skowronek 《Linear algebra and its applications》2011,435(2):361-370
In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by Størmer. Our method is based on a definition of an inner product in the space of linear maps between two algebras of operators and the fact that the Jamio?kowski-Choi isomorphism is an isometry. We consider a slightly modified class of cones, although not substantially different from the original mapping cones by Størmer. Using the new approach, several known results are proved faster and often in more generality than before. For example, the dual of a mapping cone turns out to be a mapping cone as well, without any additional assumptions. The main result of the paper is a characterization of cones with a mapping cone symmetry, saying that a given map is an element of such cone if and only if the composition of the map with the conjugate of an arbitrary element in the dual cone is completely positive. A similar result was known in the case where the map goes from an algebra of operators into itself and the cone is a symmetric mapping cone. Our result is proved without the additional assumptions of symmetry and equality between the domain and the target space. We show how it gives a number of older results as a corollary, including an exemplary application. 相似文献
9.
V. T. Khudalov 《Mathematical Notes》2000,68(5-6):640-643
It is proved that the tensor product of two linear operators is a cone summing operator (respectively, order bounded operator) if and only if both operators are cone summing (respectively, order bounded). 相似文献
10.
We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to several other interesting properties in symmetric tensor spaces.We then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius norm function of a symmetric tensor.Furthermore,we characterize the symmetric positive semidefinite tensor(SDT)cone by employing the properties of linear operators,design some face structures of its dual cone,and analyze its relationship to many other tensor cones.In particular,we show that the cone is self-dual if and only if the polynomial is quadratic,give specific characterizations of tensors that are in the primal cone but not in the dual for higher order cases,and develop a complete relationship map among the tensor cones appeared in the literature. 相似文献
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12.
In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed
expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector
space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich’s extension,
the answer is easily extracted from the general result. In combination with (Bordag et al. in Commun. Math. Phys. 182(2):371–393,
1996), a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on
the generalized cone can be obtained. 相似文献
13.
《Journal of Functional Analysis》1987,72(2):279-319
The Weyl definition of pseudodifferential operators lends itself in a natural way to generalizations to hermitian symmetric spaces. The boundedness of operators obtained in the case of the domain BD I (q = 2) is proven, as a major step towards the development of a symbolic calculus of operators on the light cone. 相似文献
14.
We derive asymptotic properties for the heat kernel of elliptic cone (or Fuchs type) differential operators on compact manifolds
with boundary. Applications include asymptotic formulas for the heat trace, counting function, spectral function, and zeta
function of cone operators.
The author was supported in part by a Ford Foundation Fellowship. 相似文献
15.
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of
certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces.
We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal
operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces. 相似文献
16.
Nguyen Thanh Qui 《Journal of Optimization Theory and Applications》2014,161(2):398-429
This paper investigates generalized differentiation of normal cone operators to parametric smooth-boundary sets in Asplund spaces. We obtain formulas for computing the Fréchet and Mordukhovich coderivatives of such normal cone operators. We also give several examples to illustrate how the formulas can be used in practical calculations and applications. 相似文献
17.
Salihah Alwadani Heinz H. Bauschke Walaa M. Moursi Xianfu Wang 《Operations Research Letters》2018,46(6):585-587
Aragón Artacho and Campoy recently proposed a new method for computing the projection onto the intersection of two closed convex sets in Hilbert space; moreover, they proposed in 2018 a generalization from normal cone operators to maximally monotone operators. In this paper, we complete this analysis by demonstrating that the underlying curve converges to the nearest zero of the sum of the two operators. We also provide a new interpretation of the underlying operators in terms of the resolvent and the proximal average. 相似文献
18.
Let E{{\mathcal E}} be a real Banach space of operators ordered by a cone K{{\mathcal K}}. We give a sufficient condition for that each chain which is bounded above has a supremum. This condition is satisfied in
several classical cases, as for the Loewner ordering on the space of all symmetric operators on a Hilbert space, for example. 相似文献
19.
Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy
of symbols. The symbolic structure is responsible for ellipticity and for the nature of parametrices within an algebra of
“edge-degenerate” pseudo-differential operators. The edge symbolic component of that hierarchy takes values in boundary value
problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in
this theory, in particular, the contribution with holomorphic operator-valued Mellin symbols. We establish a calculus in a
framework of “twisted homogeneity” that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces.
We then derive an equivalent representation with a particularly transparent composition behaviour. 相似文献
20.
Christian Sadel 《Annales Henri Poincare》2013,14(4):737-773
A tree-strip of finite cone type is the product of a tree of finite cone type with a finite set. We consider random Schrödinger operators on these tree-strips, similar to the Anderson model. We prove that for small disorder, the spectrum is almost surely, purely, absolutely continuous in a certain set. 相似文献