Search results for "Functional analysis"
showing 10 items of 1059 documents
Fréchet Spaces of Holomorphic Functions without Copies of l 1
1996
Let X be a Banach space. Let Hw*(X*) the Frechet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.
Thin Points of Brownian Motion Intersection Local Times
2005
Let \(\ell \) be the projected intersection local time of two independent Brownian paths in \(\mathbb{R}^d \) for d = 2, 3. We determine the lower tail of the random variable \(\ell \)(B(0, 1)), where B(0, 1) is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.
A Lebesgue-type decomposition for non-positive sesquilinear forms
2018
A Lebesgue-type decomposition of a (non necessarily non-negative) sesquilinear form with respect to a non-negative one is studied. This decomposition consists of a sum of three parts: two are dominated by an absolutely continuous form and a singular non-negative one, respectively, and the latter is majorized by the product of an absolutely continuous and a singular non-negative forms. The Lebesgue decomposition of a complex measure is given as application.
A note on Fréchet and approximate subdifferentials of composite functions
1994
The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.
Vertical spectrum of the C2H 2+ system. An open shell (SC)2-CAS-SDCI study
2003
The open shell (SC)(2)-CAS-SDCI method along with a basis set of atomic natural orbitals (ANO) has been applied for calculating the main ionization potentials of acetylene, as well as the manifold of excited states of the different symmetries up to 32 eV. In this method, the single and double excitations of a CAS space are generated and the corresponding CI matrix is corrected by means of the (SC)(2) procedure that cancels the size-extensivity error and adds some high order contributions. The mean absolute error for the outer-valence X (2)Pi(u)(1pi(u) (-1)), A (2)Sigma(g) (+)(3sigma(g) (-1)), and B (2)Sigma(u) (+)(2sigma(u) (-1)) states, and the inner-valence C (2)Sigma(g) (+)(2sigma(g) (-1…
Modeling and Performance Analysis of Channel Assembling in Multichannel Cognitive Radio Networks With Spectrum Adaptation
2012
[EN] To accommodate spectrum access in multichannel cognitive radio networks (CRNs), the channel-assembling technique, which combines several channels together as one channel, has been proposed in many medium access control (MAC) protocols. However, analytical models for CRNs enabled with this technique have not been thoroughly investigated. In this paper, two representative channel-assembling strategies that consider spectrum adaptation and heterogeneous traffic are proposed, and the performance of these strategies is evaluated based on the proposed continuous-time Markov chain (CTMC) models. Moreover, approximations of these models in the quasistationary regime are analyzed, and closed-fo…
Lazy consensus for networks with unknown but bounded disturbances
2007
We consider stationary consensus protocols for networks of dynamic agents. The measure of the neighbors' state is affected by Unknown But Bounded disturbances. Here the main contribution is the formulation and solution of what we call the isin-consensus problem, where the states are required to converge in a tube of ray isin asymptotically or in finite time.
Rejection-Free Monte Carlo
2019
So far, we have been using the rejection Monte Carlo algorithms. To remind us, the algorithms proceed from state x to possible state \(x'\) as outlined in Algorithm 1.
Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation
2013
From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attracto…
Dynamic Channel Aggregation Strategies in Cognitive Radio Networks with Spectrum Adaptation
2011
In cognitive radio networks, channel aggregation techniques which combine several channels together as one channel have been proposed in many MAC protocols. In this paper, spectrum adaptation is proposed in channel aggregation and two strategies which dynamically adjust channel occupancy of ongoing traffic flows are further developed. The performance of these strategies is evaluated using continuous time Markov chain models. Moreover, models in the quasi-stationary regime are analyzed and the closed-form capacity expression is derived in this regime. Numerical results demonstrate that the capacity of the secondary network can be improved by using channel aggregation with spectrum adaptation.