Showing papers on "Multiplication operator published in 1996"
TL;DR: In this article, the authors study the behavior of fL n : n 1g for HH older-continuous functions and show that the sequence is (uniformly) norm-bounded in the space of HH older continuous functions for suuciently small exponent.
Abstract: Let T be a rational function of degree 2 on the Riemann sphere. Denote L the transfer operator of a HH older-continuous function on its Julia set J = J(T) satisfying P(T;) > sup z2J (z). We study the behavior of fL n : n 1g for HH older-continuous functions and show that the sequence is (uniformly) norm-bounded in the space of HH older-continuous functions for suuciently small exponent. As a consequence we obtain that the density of the equilibrium measure for with respect to the exppP(T;) ? ]-conformal measure is HH older-continuous. We also prove that the rate of convergence of L n to this density in sup-norm is O ? exp(? p n). >From this we deduce the central limit theorem for .
121 citations
TL;DR: In this article, the authors studied symmetric operator matrices in the product of Hilbert spaces H = H 1×H 2, where the entries are not necessarily bounded operators, under suitable assumptions the closure Lo exists and is a self-adjoint operator in H. Under the assumption that there exists a real number β < inf p(A) such that M(β)<< 0, it follows that β e p(Lo).
Abstract: The authors study symmetric operator matrices
in the product of Hilbert spaces H = H1×H2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure Lo exists and is a selfadjoint operator in H. With Lo, the closure of the transfer function
is considered. Under the assumption that there exists a real number β < inf p(A) such that M(β)<< 0, it follows that β e p(Lo). Applying a factorization result of A.I. Virozub and V.I. Matsaev [VM] to the holomorphic operator function M(λ, the_spectral subspaces of Lo corresponding to the intervals ] — ∞, β] and [β, ∞[ and the restrictions of Lo to these subspaces are characterized. Similar results are proved for operator matrices
which are symmetric in a Krein space.
78 citations
TL;DR: In this article, a mathematically rigorous definition of the one-dimensional Schrodinger operator -d(2)/dx(2)-gamma/x is given, and it is proven that the domain of the operator is defined by the boundary conditions connecting the values of the function on the left and right half-axes.
Abstract: a mathematically rigorous definition of the one-dimensional Schrodinger operator -d(2)/dx(2)-gamma/x is given, It is proven that the domain of the operator is defined by the boundary conditions connecting the values of the function on the left and right half-axes. The investigated operator is compared with the Schrodinger operator containing the Coulomb potential -gamma/x.
51 citations
01 Jun 1996
TL;DR: In this paper, the maximal operator space structure which can be put on a normed space was shown to be Ω(min(X), MAX(y)) = Γ 2(X, Y) and applied to prove some Grothendieck-type inequalities and some new estimates on spans of free unitaries.
Abstract: We obtain some new results about the maximal operator space structure which can be put on a normed space. These results are used to prove some dilation results for contractive linear maps from a normed space into B(H). Finally, we prove CB(MIN(X), MAX(y)) = Γ2(X, Y) and apply this result to prove some new Grothendieck-type inequalities and some new estimates on spans of “free” unitaries.
46 citations
TL;DR: In this article, the authors consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity and show that the latter holds in quantum gravity as well, though special care should be taken regarding the physical meaning of fixing geodesic distances.
43 citations
TL;DR: The real interpolation operator space of parameters (1/2, 2) between an operator space and its antidual is completely isomorphic to an operator Hilbert space OH ( I ), discovered recently by G. Pisier as discussed by the authors.
34 citations
TL;DR: It is shown that, for two variables, the Hermitian and unitary operator correspondences can be used consistently and interchangeably if and only if the variables are dual.
Abstract: Fundamental to the theory of joint signal representations is the idea of associating a variable, such as time or frequency, with an operator, a concept borrowed from quantum mechanics. Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parameterized unitary operator. It is well known that the eigenfunctions of the unitary operator define a signal representation which is invariant to the effect of the unitary operator on the signal, and is hence useful when such changes in the signal are to be ignored. However, for detection or estimation of such changes, a signal representation covariant to them is needed. Using well-known results in functional analysis, we show that there always exists a translationally covariant representation; that is, an application of the operator produces a corresponding translation in the representation. This is a generalization of a recent result in which a transform covariant to dilations is presented. Using Stone's theorem, the "covariant" transform naturally leads to the definition of another, unique, dual parameterized unitary operator. This notion of duality, which we make precise, has important implications for joint distributions of arbitrary variables and their interpretation. In particular, joint distributions of dual variables are structurally equivalent to Cohen's class of time-frequency representations, and our development shows that, for two variables, the Hermitian and unitary operator correspondences can be used consistently and interchangeably if and only if the variables are dual.
33 citations
TL;DR: A simple model for measuring the discrete Q function is presented, which is non-negative and can be measured directly in particular experiments, whereas the P function corresponds to the diagonal form of the density operator in an overcomplete basis.
Abstract: Using discrete displacement-operator expansion, s-parametrized phase-space functions associated with the operators in a finite-dimensional Hilbert space are introduced and their properties are studied. In particular, the phase-space functions associated with the density operator can be regarded as quasidistributions whose properties are similar to those of the well-known quasidistributions in the continuous phase space. So the Q function ( s521) is non-negative and can be measured directly in particular experiments, whereas the P function ( s51) corresponds to the diagonal form of the density operator in an overcomplete basis. Except for the W function ( s50), the introduction of discrete phase-space functions requires the choice of a special reference state. We finally present a simple model for measuring the discrete Q function. @S1050
32 citations
TL;DR: In this paper, the spectral properties of a multiplication operator in the space Lp(X)m which is given by an m by m matrix of measurable functions are studied. But their particular interest is directed to the eigenvalues and the isolated spectral points which turn out to be eigen values.
Abstract: In this note we study the spectral properties of a multiplication operator in the space Lp(X)m which is given by an m by m matrix of measurable functions. Our particular interest is directed to the eigenvalues and the isolated spectral points which turn out to be eigenvalues. We apply these results in order to investigate the spectrum of an ordinary differential operator with so called “floating singularities”.
TL;DR: It is shown that the norm of a composition operator on the classical Hardy space H 2 cannot be computed using only the set of H 2 reproducing kernels, answering a question raised by Cowen and MacCluer.
Abstract: We show that the norm of a composition operator on the classical Hardy space H 2 cannot be computed using only the set of H 2 reproducing kernels, answering a question raised by Cowen and MacCluer.
TL;DR: It is argued that the present method is more suitable for removing the effects of atmospheric turbulence than the conventional procedures because it is ideally suited for resolving spectral power laws.
TL;DR: In this paper, the convolution operator on a finite interval defined on a space of L 2 functions is studied by relating it to a singular integral operator acting on a system of two parallel straight lines in the complex plane ℂ.
Abstract: The convolution operator on a finite interval defined on a space ofL2 functions is studied by relating it to a singular integral operator acting on a space of functions defined on a system of two parallel straight lines in the complex plane ℂ. The approach followed in the paper applies both to the case where the Fourier transform of the kernel functions is anL∞ function and to the case where the kernel function is periodic, thus yielding a unified treatment of these two classes of kernel functions. In the non-periodic case it is possible, for a special class of kernel functions, to study the invertibility property of the operator giving an explicit formula for the inverse. An example is presented and generalizations are suggested.
TL;DR: In this article, it was shown that every one-dimensional extension of a bitriangular operator has a cyclic commutant, and if the extension is an algebraic operator, then the weakly closed algebra W(T) generated by T has a separating vector.
Abstract: We prove that every one-dimensional extension of a bitriangular operator has a cyclic commutant. We also prove that ifT is an extension of a bitriangular operator by an algebraic operator, then the weakly closed algebraW(T) generated byT has a separating vector.
TL;DR: Even and odd phase coherent states associated with the Hermetian phase operator theory are introduced in this article in terms of the creation operation of the phase quanta defined in a finite-dimensional phase state space.
Abstract: Even and odd phase coherent states associated with the Hermetian phase operator theory are introduced in terms of the creation operation of the phase quanta defined in a finite-dimensional phase state space. Some mathematical and physical properties of these quantum states are studied in some detail. It is shown that the even phase coherent states together with the odd ones build an overcomplete Hilbert space. Even and odd coherent-state formalism of the Pegg - Barnett phase operator is given in terms of the projection operator in the even and odd phase coherent-state space. The number - phase uncertainty relation is investigated for these quantum states. It is shown that even and odd phase coherent states are not minimum uncertainty and intelligent states for the number and phase operators.
TL;DR: This paper proposes a new method using the discrete del operator which is a coordinate-free differential operator in discrete space which is useful in nonmemorizing and in easy coding in FEM.
Abstract: Generally speaking, finite-element methods in computational fluid dynamics are universal, but uneconomical. In the present paper, in order to overcome this defect in FEM, we propose a new method using the discrete del operator which is a coordinate-free differential operator in discrete space. This operator in discrete space is defined as an element average of the gradient of the shape function, and it has three characteristics: orthogonality, identity and symmetry. Furthermore, the discrete del operator is useful in nonmemorizing and in easy coding. Since the analytical expression of the discrete del operator is a vector in two or three dimensions, the natural description of programing becomes objective and compact, which is more understandable for nonspecialists of CFD.
TL;DR: In this paper, a model for a condenser microphone with a rigid cylinder closed on the bottom by a membrane and on the top by a rigid plate is presented. But the model is restricted to two chambers with holes.
Abstract: A realistic model for a condenser microphone is theoretically investigated. The model consists of a rigid cylinder closed on the bottom by a membrane and on the top by a rigid plate. The cylinder is divided into two chambers by an electrode with a number of small holes. This coupled acoustic system is mathematically treated by an operator formalism. Each part of the system (outer space, membrane, electrode, two chambers) corresponds a linear operator in a Hilbert space. The interfaces (membrane, electrode with holes) correspond to state vectors in this Hilbert space. Applying Green’s integral formula leads to a system of equations in this space, corresponding conventionally to integral equations with Green’s functions as kernels. By approximating the operators of the two chambers by multiples of the identity operator (i.e., conventionally replacing the singular Green’s function by multiples of the Dirac delta function) it is possible to solve the problem analytically, taking into account exactly the patte...
TL;DR: In this paper, it was shown that the space of all ν-equivariant complex valued functions over the N -particle configuration space cannot be identified with the quantum states of the system, since the former is not invariant under the evolution operator.
TL;DR: In this article, a hybrid-streamline-upwind finite-element method was proposed, which is based on the finite analytic method developed in the field of the finite difference method.
Abstract: In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them interpolates accurately the functions appearing in convection-dominated flows, the other becomes a hybrid-streamline-upwind weighting function. Furthermore, we define a discrete del operator for the reduction of memory storage in the computer. As a result, we achieve simplicity of formulation and high-speed calculation of the finite-element method.
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TL;DR: In this article, it is shown that when the final state is connected with the initial one by means of a Bogoliubov transformation, which does not include the single-mode rotation operator, the mean value of created particles is conserved.
Abstract: Taking into account a neutral massive scalar field minimally coupled to gravity, in a Robertson-Walker metric, it is shown that when the final state is connected with the initial one by means of a Bogoliubov transformation, which does not include the single-mode rotation operator, the mean value of created particles is conserved. When the rotation operator is considered, it is still possible to use the approach of single-mode squeezed operators and get the entropy as the logarithm of the created particles.
Journal Article•
TL;DR: In this article, a hybrid-streamline-upwind finite-element method is proposed to obtain an optimal shape function, which is based on the finite analytic method developed in the field of finite difference analysis.
Abstract: In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference analysis. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them accurately interpolates the functions appearing in convection-dominated flows, and the other becomes a hybrid-streamline-upwind weight function. Furthermore, we define a discrete del operator for the reduction of memory storage in computers. As a result, we achieve simplicity of formulation and high-speed calculation in the finite-element method.
Journal Article•
TL;DR: In this article, a differential operator by an admissible group in the space L 2 (ℝm,P) was constructed and its properties were studied in the presence of admissible groups.
Abstract: We construct a differential operator by an admissible group in the space L
2 (ℝm,P)and study its properties.
TL;DR: In this article, the Frobenius-Perron operator associated with a nonsingular transformation S : X → X on a σ-finite measure space X is the product of an isometry and a weak contraction.
TL;DR: An efficient algorithm to implement parallel integer multiplication by a combination of parallel additions, shifts and reads from a memory-resident lookup table dedicated to squares is proposed.