Search results for "Hilbert"
showing 10 items of 331 documents
A concise review on pseudo-bosons, pseudo-fermions and their relatives
2017
We review some basic definitions and few facts recently established for $\D$-pseudo bosons and for pseudo-fermions. We also discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional Hilbert space. Some examples are described in details.
Some remarks on unconditionally convergent multipliers
2017
We present some results concerning the representation of unconditionally convergent multipliers, including a reformulation of a conjecture of Balazs and Stoeva.
A new mathematical tool for an exact treatment of open quantum system dynamics
2005
A new method to obtain an operatorial exact solution of a wide class of Markovian master equations is presented. Its key point is the existence of a constant of motion partitioning the Hilbert space into finite-dimensional subspaces. The consequent possibility of representing the reduced density operator as a block diagonal matrix is shown. Each “block operator” evolves under the action of a non-unitary operator explicitly derived. Our mathematical approach is illustrated applying it to simple physical systems.
Orbits of bounded bijective operators and Gabor frames
2020
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are often used in applications. More precisely, the paper deals with a question posed in the last years by Christensen and Hasannasab about the existence of overcomplete Gabor frames, with some ordering over $\mathbb{Z}$, which are orbits of bounded operators on $L^2(\mathbb{R})$. Two classes of overcomplete Gabor frames which cannot be ordered over $\mathbb{Z}$ and represented by orbits of operators in $GL(L^2(\mathbb{R}))$ are given. Some results about opera…
Damage identification by a modified Ant Colony Optimization for not well spaced frequency systems
2011
Recently, it has been shown , that a damage detection strategy based on a proper functional calculated on the analytical signal of the structural dynamical response, consents to identify very low damage level. In this regard, they stressed the efficiency of Hilbert Transform to obtain the analytical response representation that shows more sensitivity for predicting damage with respect to the simple signal response. Then, a damage identification procedure based on the minimization of the difference between theoretical and measured data was proposed with satisfactory results. Unfortunately, this procedure, since the need of use of band pass filter around the natural frequency of the system, f…
The contributions of Hilbert and Dehn to non-Archimedean geometries and their impact on the Italian school
2007
In this paper we investigate the contribution of Dehn to the development of non- Archimedean geometries. We will see that it is possible to construct some models of non- Archimedean geometries to prove the independence of the continuity axiom and we will study the interrelations between Archimede’s axiom and Legendre‘s theorems. Some of these interrelations were studied also by Bonola who was one of the very few italian scholars to really appreciate Dehn’s work. We will see that, if Archimede’s axiom does not hold, the hypothesis on the existence and the number of parallel lines through a point is not related to the hypothesis on the sum of the inner angles a triangle. Hilbert himself retur…
Some models of geometries after Hilbert’s Grundlagen
2010
Sono descritti alcuni dei principali modelli di geometrie non desarguesiane e non archimedee Abstract: We investigate the contribution of Max Dehn to the development of non-Archimedean geometries and the contribution of his student Ruth Moufang to the development of non-Desarguesian geometries.
Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed
2020
Non-Markovian effects can speed up the dynamics of quantum systems while the limits of the evolution time can be derived by quantifiers of quantum statistical speed. We introduce a witness for characterizing the non-Markovianity of quantum evolutions through the Hilbert-Schmidt speed (HSS), which is a special type of quantum statistical speed. This witness has the advantage of not requiring diagonalization of evolved density matrix. Its sensitivity is investigated by considering several paradigmatic instances of open quantum systems, such as one qubit subject to phase-covariant noise and Pauli channel, two independent qubits locally interacting with leaky cavities, V-type and $\Lambda $-typ…
A Note on Riesz Bases of Eigenvectors of Certain Holomorphic Operator-Functions
2001
Abstract Operator-valued functions of the form A (λ) ≔ A − λ + Q(λ) with λ ↦ Q(λ)(A − μ)− 1 compact-valued and holomorphic on certain domains Ω ⊂ C are considered in separable Hilbert space. Assuming that the resolvent of A is compact, its eigenvalues are simple and the corresponding eigenvectors form a Riesz basis for H of finite defect, it is shown that under certain growth conditions on ‖Q(λ)(A − λ)− 1‖ the eigenvectors of A corresponding to a part of its spectrum also form a Riesz basis of finite defect. Applications are given to operator-valued functions of the form A (λ) = A − λ + B(λ − D)− 1C and to spectral problems in L2(0, 1) of the form −f″(x) + p(x, λ)f′(x) + q(x, λ)f(x) = λf(x…
On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces
2016
In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.