Search results for "Tensor product"
showing 10 items of 58 documents
Tensor-product states and local indistinguishability: an optical linear implementation
2000
In this paper we investigate the properties of distinguishability of an orthogonal set of product states of two three level particle system by a simple class of joint measures. Here we confine ourselves to a system of analysis built up of linear elements, such as beam splitters and phase shifters, delay lines, electronically switched linear devices and auxiliary photons. We present here the impossibility of realization of a perfect never falling analyzer with this tools.
Generating harmonic surfaces for interactive design
2014
Abstract A method is given for generating harmonic tensor product Bezier surfaces and the explicit expression of each point in the control net is provided as a linear combination of prescribed boundary control points. The matrix of scalar coefficients of these combinations works like a mould for harmonic surfaces. Thus, real-time manipulation of the resulting surfaces subject to modification of prescribed information is possible.
Singletons on AdSn
2000
We define the singletons for the invariance group \( {\overline S _n} = {\overline {SO} _0}\left( {2,n - 1} \right) \)) of the AdS n space-time. We write down some of their important properties and characterizations. It is found that the tensor product of singletons of spin 0 or 1/2 decomposes into representations that are a kind of massless representations of S n . Other kinds of massless representations, related to singletons, are also studied and a comparison is made. Various Gupta-Bleuler triplets are constructed for singletons and for massless representations.
New results concerning Chebyshev–Grüss-type inequalities via discrete oscillations
2014
The classical form of Gruss' inequality was first published by G. Gruss and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to consider some new bivariate Chebyshev-Gruss-type inequalities via discrete oscillations and to apply them to different tensor products of linear (not necessarily) positive, well-known operators. We also compare the new inequalities with some older results. In the end we give a Chebyshev-Gruss-type inequality with discrete oscillations for more than two functions.
Traced tensor norms and multiple summing multilinear operators
2016
[EN] Using a general tensor norm approach, our aim is to show that some distinguished classes of summing operators can be characterized by means of an 'order reduction' procedure for multiple summing multilinear operators, which becomes the keystone of our arguments and can be considered our main result. We work in a tensor product framework involving traced tensor norms and the representation theorem for maximal operator ideals. Several applications are given not only to multi-ideals, but also to linear operator ideals. In particular, we get applications to multiple p-summing bilinear operators, (p, q)-factorable linear operators, tau(p)-summing linear operators and absolutely p-summing li…
The Partial Inner Product Space Method: A Quick Overview
2010
Many families of function spaces play a central role in analysis, in particular, in signal processing (e.g., wavelet or Gabor analysis). Typical are spaces, Besov spaces, amalgam spaces, or modulation spaces. In all these cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators. It turns out that all these space families are, or contain, scales or lattices of Banach spaces, which are special cases ofpartial inner product spaces(PIP-spaces). In this context, it is often said that such families should be taken as a whole and operators, bases, and frames on them should be defined globally, for the whole family, instead o…
Some Properties of Massless Particles in Arbitrary Dimensions
1998
Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group [Formula: see text] are investigated for n≥2. It is found that, for space-time dimensions n≥3, the situation is quite similar to the one of the n=4 case for Sn-massless representations of the n-De Sitter group [Formula: see text]. These representations are the restrictions of the singletons of [Formula: see text]. The main difference is that they are not contained in the tensor product of two UIRs with the same sign of energy when n>4, whereas it is the case for another kind of massless representations. Finally some examples of Gupta–Bleuler triplets are given for arbitrary spin and…
Factorization in closed string field theory
1994
Abstract The so long made assumption, that a general closed-string vertex operator V should be built as a product of left- and right-moving vertex operators, rests on the fact that the closed-string Fock spce is constructed as a tensor product of left- and right-moving open-string Fock spaces. In this letter we will relax this assumption by proving that factorization of closed-string vertices is a general rule.
The Schur property on projective and injective tensor products
2008
The problem of whether the Schur property is passed from a Banach space to its (symmetric) projective n-fold tensor product is reformu lated in the language of polynomial ideals. As a result, a very closely related question is solved in the negative. It is also proved that the injective tensor product of infrabarrelled locally convex spaces with the Schur property has the Schur property as well.
The Period Isomorphism
2017
The aim of this section is to define well-behaved isomorphisms between singular and de Rham cohomology of algebraic varieties.