Search results for "JOINT"

showing 10 items of 1472 documents

QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS

1995

The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.

Discrete mathematicsHilbert manifoldHilbert spaceStatistical and Nonlinear PhysicsRigged Hilbert spaceOperator spaceCompact operator on Hilbert spaceAlgebraPOVMsymbols.namesakeOperator algebraHermitian adjointsymbolsMathematical PhysicsMathematicsReviews in Mathematical Physics
researchProduct

Perturbations of surjective convolution operators

2002

Let μ 1 and μ 2 be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator f → μ 1 *f is surjective when it acts on a space of functions or (ultra)distributions, and we investigate whether the perturbed convolution operator f→ (μ 1 + μ 2 ) * f is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.

Discrete mathematicsLaplace transformApplied MathematicsGeneral MathematicsDisjoint setsOperator theorySpace (mathematics)ConvolutionSurjective functionsymbols.namesakeDistribution (mathematics)Fourier transformsymbolsMathematicsProceedings of the American Mathematical Society
researchProduct

Every triangle-free induced subgraph of the triangular lattice is(5m,2m)-choosable

2014

A graph G is (a,b)-choosable if for any color list of size a associated with each vertex, one can choose a subset of b colors such that adjacent vertices are colored with disjoint color sets. This paper proves that for any integer m>=1, every finite triangle-free induced subgraph of the triangular lattice is (5m,2m)-choosable.

Discrete mathematicsMathematics::CombinatoricsApplied Mathematics010102 general mathematicsInduced subgraphNeighbourhood (graph theory)0102 computer and information sciencesDisjoint sets01 natural sciencesGraphVertex (geometry)CombinatoricsComputer Science::Discrete Mathematics010201 computation theory & mathematicsDiscrete Mathematics and CombinatoricsHexagonal lattice0101 mathematicsMathematicsDiscrete Applied Mathematics
researchProduct

The support localization property of the strongly embedded subspaces of banach function spaces

2015

[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulflled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsVolterra operatorFunctional analysisDisjoint sequenceStrongly embedded subspaceFunction spaceGeneral MathematicsLorentz transformationVector measure integrationBanach function spaceLinear subspacesymbols.namesakesymbolsInterpolation spaceBirnbaum–Orlicz spaceLp spaceMATEMATICA APLICADAMathematics
researchProduct

Transportation cost inequalities on path and loop groups

2005

AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).

Discrete mathematicsPath (topology)Adjoint representationLie groupGirsanov theoremSpace (mathematics)Action (physics)Heat measuresLoop groupsLoop (topology)Loop groupLie algebraWasserstein distanceAnalysisMathematicsH-distanceJournal of Functional Analysis
researchProduct

A Polynomial Quantum Query Lower Bound for the Set Equality Problem

2004

The set equality problem is to tell whether two sets A and B are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any ω(1) query lower bound when sets A and B are given by quantum oracles. We will show that any error-bounded quantum query algorithm that solves the set equality problem must evaluate oracles \(\Omega(\sqrt[5]{\frac{n}{\ln n}})\) times, where n=|A|=|B|.

Discrete mathematicsPolynomial (hyperelastic model)CombinatoricsOpen problemGraph isomorphism problemTheoryofComputation_GENERALCollision problemQuantum algorithmDisjoint setsIsomorphismUpper and lower boundsMathematics
researchProduct

The Separable Complementation Property and Mrówka Compacta

2017

We study the separable complementation property for $C(K_{\cal A})$ spaces when $K_{\cal A}$ is the Mr\'owka compact associated to an almost disjoint family ${\cal A}$ of countable sets. In particular we prove that, if ${\cal A}$ is a  generalized ladder system,  then $C(K_{\cal A})$ has the separable complementation property ($SCP$ for short) if and only if it has the controlled version of this property. We also show that, when ${\cal A}$ is  a maximal generalized ladder system, the space $C(K_{\cal A})$ does not enjoy the $SCP$.

Discrete mathematicsProperty (philosophy)Countable setDisjoint setsSpace (mathematics)MathematicsSeparable spaceJournal of Mathematics Research
researchProduct

Non-integrality of the PI-exponent of special Lie algebras

2013

If L is a special Lie algebra over a field of characteristic zero, its sequence of codimensions is exponentially bounded. The PI-exponent measures the exponential rate of growth of such sequence and here we give a first example of a special Lie algebra whose (upper and lower) PI-exponent is non-integer.

Discrete mathematicsPure mathematicsAdjoint representation of a Lie algebraApplied MathematicsSimple Lie groupLie algebraLie algebraReal formKilling formAffine Lie algebraMathematicsLie conformal algebraGraded Lie algebra
researchProduct

On the Codimension Growth of Finite-Dimensional Lie Algebras

1999

Abstract We study the exponential growth of the codimensions cn(L) of a finite-dimensional Lie algebra L over a field of characteristic zero. We show that if the solvable radical of L is nilpotent then lim n → ∞ c n ( L ) exists and is an integer.

Discrete mathematicsPure mathematicsAdjoint representation of a Lie algebraNilpotentAlgebra and Number TheorySimple Lie groupUniversal enveloping algebraKilling formAffine Lie algebraMathematicsLie conformal algebraGraded Lie algebraJournal of Algebra
researchProduct

LEFT INVARIANT COMPLEX STRUCTURES ON NILPOTENT SIMPLY CONNECTED INDECOMPOSABLE 6-DIMENSIONAL REAL LIE GROUPS

2007

Integrable complex structures on indecomposable 6-dimensional nilpotent real Lie algebras have been computed in a previous paper, along with normal forms for representatives of the various equivalence classes under the action of the automorphism group. Here we go to the connected simply connected Lie group G0 associated to such a Lie algebra 𝔤. For each normal form J of integrable complex structures on 𝔤, we consider the left invariant complex manifold G = (G0, J) associated to G0 and J. We explicitly compute a global holomorphic chart for G and we write down the multiplication in that chart.

Discrete mathematicsPure mathematicsAdjoint representation of a Lie algebraRepresentation of a Lie groupGeneral MathematicsSimple Lie groupLie algebraAdjoint representationReal formMathematicsLie conformal algebraGraded Lie algebraInternational Journal of Algebra and Computation
researchProduct