Showing papers on "Multiplication operator published in 1998"

Non-commutative vector valued Lp-spaces and completely p-summing maps

Abstract: Let $E$ be an operator space in the sense of the theory recently developed by Blecher-Paulsen and Effros-Ruan. We introduce a notion of $E$-valued non commutative $L_p$-space for $1 \leq p < \infty$ and we prove that the resulting operator space satisfies the natural properties to be expected with respect to e.g. duality and interpolation. This notion leads to the definition of a ``completely p-summing" map which is the operator space analogue of the $p$-absolutely summing maps in the sense of Pietsch-Kwapie\'n. These notions extend the particular case $p=1$ which was previously studied by Effros-Ruan.

A Local Regularization Operator for Triangular and Quadrilateral Finite Elements

Abstract: This paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes. This operator is a variant of the regularization operator of Clement; however, ours is constructed via a local projection in a reference domain. We prove in this paper that it has the same optimal approximation properties as the standard interpolation operator, and we present some applications.

Interacting Fock Spaces and Gaussianization of Probability Measures

Abstract: We prove that any probability measure on ℝ, with moments of all orders, is the vacuum distribution, in an appropriate interacting Fock space, of the field operator plus (in the nonsymmetric case) a function of the number operator. This follows from a canonical isomorphism between the L2-space of the measure and the interacting Fock space in which the number vectors go into the orthogonal polynomials of the measure and the modified field operator into the multiplication operator by the x-coordinate. A corollary of this is that all the momenta of such a measure are expressible in terms of the Szego–Jacobi parameters, associated to its orthogonal polynomials, by means of diagrams involving only noncrossing pair partitions (and singletons, in the nonsymmetric case). This means that, with our construction, the combinatorics of the momenta of any probability measure (with all moments) is reduced to that of a generalized Gaussian. This phenomenon we call Gaussianization. Finally we define, in terms of the Szego–...

Reduced models in the medium frequency range for general dissipative structural-dynamics systems

Abstract: This paper presents a theoretical approach for constructing a reduced model in the medium-frequency range in the area of structural dynamics for a general three-dimensional anisotropic and inhomogeneous viscoelastic bounded medium. All the results presented can be used for beams, plates and shells. The boundary value problem in the frequency domain and its variational formulation are presented. For a given medium-frequency band, an energy operator which is intrinsic to the dynamical system is introduced and mathematically studied. This energy operator depends on the dissipative part of the dynamical system. It is proved that this operator is a positive-definite symmetric trace operator in a Hilbert space and that its dominant eigensubspace allows a reduced model to be constructed using the Ritz-Galerkin method. An effective construction of the dominant subspace using the subspace iteration method is developed. Finally, an example is given to validate the concepts and the algorithms.

Absence of singular spectrum for a perturbation of a two-dimensional Laplace-Beltrami operator with periodic electromagnetic potential

Abstract: Let be a lattice on . We consider a metric g, a one-form A and a real function V on , all periodic. We prove that the spectrum of the Schrodinger operator on , is absolutely continuous.

Representation-theoretic aspects of two-dimensional quantum systems in singular vector potentials: Canonical commutation relations, quantum algebras, and reduction to lattice quantum systems

Abstract: Some representation-theoretic aspects of a two-dimensional quantum system of a charged particle in a vector potential A, which may be singular on an infinite discrete subset D of R2 are investigated. For each vector v in a set V(D)⊂R2\{0}, the projection Pv of the physical momentum operator P≔p−αA to the direction of v is defined by Pv≔v⋅P as an operator acting in L2(R2), where p=(−iDx,−iDy)[(x,y)∈R2] with Dx (resp., Dy) being the generalized partial differential operator in the variable x (resp., y) and α∈R is a parameter denoting the charge of the particle. It is proven that Pv is essentially self-adjoint and an explicit formula is derived for the strongly continuous one-parameter unitary group {eitPv}t∈R generated by the self-adjoint operator Pv (the closure of Pv), i.e., the magnetic translation to the direction of the vector v. The magnetic translations along curves in R2\D are also considered. Conjugately to Pv and Pw [w∈V(D)], a self-adjoint multiplication operator Qv,w is introduced, which is a ...

On the Essential Spectrum of a Class of Operators in Hilbert Space

Abstract: Sufficient conditions are given such that the product T1T2 of two unbounded operators in Hilbert spaces is essentially selfadjoint and that the nonzero numbers in the essential spectrum of the closure of T1T2 coincide with the nonzero numbers in the essential spectrum of T2T1. If the essential spectrum of the closure of T2T1 only consists of zero and M is a bounded operator, then several formulas for the essential spectrum of the closure of T2T1 + M are given.

Intertwining operator and $h$-harmonics associated with reflection groups

Abstract: We study the intertwining operator and h-harmonics in Dunkl's theory on h-harmonics associated with reflection groups. Based on a bio rthogonality between the ordinary harmonics and the action of the intertwining operator V on the harmonics, the main result provides a method to compute the action of the intertwining operator V on polynomials and to construct an orthonormal basis for the space of h-harmonics.

Efficient interface conditions based on a 5-point finite difference operator

Abstract: A new 5-point finite difference operator is developed for integrated optics simulations. Interfaces are taken into account accurately. The eigenvalues of the discretization matrix converge rapidly, according to O(Δx4). Implementation of the operator in a beam propagator leads to a highly efficient computation scheme.

The OI-Resolution of Operator Rough Logic

Abstract: Based on rough set theory, this paper establishes operator space [ξ*, ξ*]. It is also a subset on truth value interval [0,1]. The operators is put in the front of the formulas to produce the manyvalued logic called operator rough logic(ORL). It defines OI-valid and OI-inconsistent, OI-resolution of the logic, where OI is an abbreviation of Operator Interval. And it also proves the soundness theorem of the logic resolution.

Extending the formula to calculate the spectral radius of an operator

Abstract: In a Banach space, Gelfand’s formula is used to find the spectral radius of a continuous linear operator. In this paper, we show another way to find the spectral radius of a bounded linear operator in a complete topological linear space. We also show that Gelfand’s formula holds in a more general setting if we generalize the definition of the norm for a bounded linear operator.

Maximal inequalities and space-time regularity of stochastic convolutions

Abstract: Space-time regularity of stochastic convolution integrals J = {\int^\cdot_0 S(\cdot-r)Z(r)W(r)} driven by a cylindrical Wiener process $W$ in an $L^2$-space on a bounded domain is investigated The semigroup $S$ is supposed to be given by the Green function of a $2m$-th order parabolic boundary value problem, and $Z$ is a multiplication operator Under fairly general assumptions, $J$ is proved to be Holder continuous in time and space The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well

On the boundedness of classical operators on weighted lorentz spaces

Abstract: Conditions on weights u(A), v(A) are given so that a clas- sical operator T sends the weighted Lorentz space Lrs(vdx) into Lpq(udx). Here T is either a fractional maximal operator Ma or a fractional integral operator Ia or a Calderon-Zygmund operator. A characterization of this boundedness is obtained for Ma and Ia when the weights have some usual properties and max(r;s) i min(p;q).

The jacobi operator of real hypersurfaces in a complex space form

Abstract: Let o and A be denoted by the structure tensor field of type (1,1) and by the shape operator of a real hypersurface in a complex space form (c), c 0 respectively. The main purpose of this paper is to prove that if a real hypersurface in (c) satisfies oA = , then the structure vector field ξ is principal, where / is the Jacobi operator with respect to ξ.

Lp and operator norm estimates for the complex time heat operator on homogeneous trees

Abstract: Let X be a homogeneous tree of degree greater than or equal to three. In this paper we study the complex time heat operator Hζ induced by the natural Laplace operator on X. We prove comparable upper and lower bounds for the Lp norms of its convolution kernel hζ and derive precise estimates for the Lp–Lr operator norms of Hζ for ζ belonging to the half plane Re ζ ≥ 0. In particular, when ζ is purely imaginary, our results yield a description of the mapping properties of the Schrödinger semigroup on X. Let X be a homogeneous tree of degree q + 1, i.e., a connected graph with no loops in which every vertex is adjacent to q + 1 other vertices. Unless explicitly stated otherwise, we will assume that q ≥ 2. We will write x ∼ y if x and y are adjacent. X carries a natural distance function d, d(x, y) being the number of edges between the vertices x and y, and a natural measure, the counting measure, with respect to which we form the Lebesgue spaces L(X). On X there is also a natural Laplace operator defined by the formula Lf(x) = 1 q + 1 ∑ x∼y [f(x)− f(y)] . L is easily seen to be bounded on L(X) for every 1 ≤ p ≤ +∞, and self-adjoint on L(X), and therefore the heat operator Ht, which is spectrally defined on L(X) by Htf = ∫ σ2(L) e−tλdPλf ∀t ∈ (0,+∞) ∀f ∈ L(X), where σ2(L) denotes the L spectrum of L, and Pλ its spectral resolution, is also given by the series

One-dimensional perturbations of singular unitary operators

Abstract: Under some natural restrictions, we prove that any one-dimensional perturbation of a singular unitary operator on a Hilbert space is unitarily equivalent to a model operator on a space determined (in a certain way) by two functions from the Hardy space H2. Bibliography: 3 titles.

On the eigenstructure of linear quasi-time-invariant systems

Abstract: In this paper, the eigenstructure of a class of linear time-varying systems, termed linear quasi-time-invariant (LQTI) systems, is investigated. A system composed of dynamic devices such as linear time-varying capacitors and resistors can be an example of the class. To describe and analyze the LQTI systems effectively, a differential operator G composed of the derivative operator D and some time functions is adopted. Then, the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characterisics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. The corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency-domain analysis and design of the filters. It is also noted that the stability is determined by the position of poles in the G frequency domain, where the stable region in the complex plane is different from the classical left half s ...

On the discrete spectrum of some selfadjoint operator matrices

Abstract: This paper is devoted to the study of the discrete spectrum of selfadjoint operators, which are generated by symmetric operator matrices of the form L0 = " A B

Generation results forB-bounded semigroups

Abstract: In [3]A. Bellini-Morante defined and analysed a new one-parameter family of bounded operators which he called a B-bounded semigroup. The definition was motivated by an example from the transport theory where the evolution generated by an operator A was in a certain sense controlled by another operator B. In this paper we show that a given pair (A, B) generates a B-bounded semigroup if and only if in a certain extrapolation space related to the operator B, the closure of A generates a semigroup and we also address some related topics.

The nehari problem for the hardy space on the torus

Abstract: Communicated by Norberto Salinas Abstract. We explicitly construct functions in H 2 (T 2 ) ? which determine bounded (big) Hankel operators on H 2 (T 2 ) but are not of the form P? for any 2 L 1 (T 2 ). We use this construction to show that the norm of a Hankel operator with bounded symbol is not, in general, comparable to the distance the symbol is from H 1 (T 2 ). We also characterize the vector space quotient of symbols of bounded Hankel operators modulo those which lift to L 1 (T 2 ) in terms of a Toeplitz completion problem on vector-valued Hardy space in one-variable. 2 H 2 (T 2 ) ? , the big Hankel operator with symbol is densely defined by f = P?(f ) where f 2 H 2 (T 2 ) is a polynomial and P? : L 2 (T 2 ) ! H 2 (T 2 ) ? is the orthogonal projection onto H 2 (T 2 ) ? . Note that = P? on polynomials and the correspondence between the operator and the function P? is one-to-one. Let Hank(T 2 ) denote the space of functions 2 H 2 (T 2 ) ? for which extends to a bounded operator from H 2 (T 2 ) into L 2 (T 2 ) equipped with the operator norm,