1,535 research outputs found
New Reverse Inequalities for Normal Operators in Hilbert Spaces
No full textIn this paper, more reverse inequalities for the class of normal
operators, are established. Some of the obtained results are based on recent
reverse results for the Schwarz inequality in Hilbert spaces due to the author
Upper Bounds for the Euclidean Operator Radius and Applications
No full textThe main aim of the present paper is to establish various sharp
upper bounds for the Euclidean operator radius of an n−tuple of bounded
linear operators on a Hilbert space. The tools used are provided by several
generalisations of Bessel inequality due to Boas-Bellman, Bombieri and the
author. Natural applications for the norm and the numerical radius of bounded
linear operators on Hilbert spaces are also given
Dienstleistungen in der Neuen Ökonomie : Struktur, Wachstum und Beschäftigung ; Gutachten der Friedrich-Ebert-Stiftung
No full texthrsg. von Anja Hartman , Hans Mathieu ; Autoren: Eva Bertram, Rainer Fretschner, Anja Hartmann, Josef Hilbert, Michael R. Hübner, Anja Sophia Middendorf, Claudia Niewerth, Frank SchulteElectronic ed.: Berlin : FES, 200
Inequalities for some Functionals Associated with Bounded Linear Operators in Hilbert Spaces
No full textSome inequalities between the operator norm, numerical radius
and functional are established. New upper bounds for the nonnegative
quantity that complement some recent results of the author are given as well
Notes on Hilbert and Cauchy matrices
No full textAbstractInspired by examples of small Hilbert matrices, the author proves a property of symmetric totally positive Cauchy matrices, called AT-property, and consequences for the Hilbert matrix
Contractible Hilbert cube manifolds
No full textIn this note we give an example of a contractible Hilbert cube manifold which cannot be embedded as an open subset of the Hilbert cube Q so that its complement (in Q) lies in a face of the boundary of Q. This example provides a negative answer to a question raised by the author.</p
Discrete Hilbert-Type Inequalities
No full textDiscrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral inequality with an independent parameter. In 2004, some new extensions of Hilbert's inequality were presented by introducing two pairs of conjugate exponents and additional independent parameters. Since then, a number of new discrete Hilbert-type inequalities have arisen. In this book, the author explains how to use the way of weight coefficients and introduce specific parameters to build new discrete Hi
Damage detection in a real truss bridge using Hilbert-Huang Transform of transient vibrations
No full textStructural Health Monitoring (SHM) in bridges is an important field, which implements increasingly innovative damage detection strategies for both theoretical developments and laboratory-scale implementations. However, is very important to consider the studies of bridges in real conditions. This study presents the damage identification of a real bridge using Hilbert-Huang transform and the most recent advance in the empirical mode decomposition method (EMD) called Improvements on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN). This technique is used to decompose vibration data into intrinsic mode functions (IMF). Then, the Marginal Hilbert spectrum and phase difference were two damage features studied on a bridge where artificial damage was imposed. These artificial damage levels were applied sequentially and the vibration data was obtained by the passage of a recreation vehicle. As results, the ICEEMDAN method and proposed damage indicators demonstrate good performance to detect and locate damages under transient vibration loads on a real bridge.The first author acknowledges the support received from Ministry of Education of Peru with the National Scholarship and Educational Loan Program PRONABEC - President of the Republic Scholarship. The authors wish to express their gratitude to professor Woo Kim of the Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan for the generous sharing of the steel truss bridge data assessed within this study.Postprint (published version
Some more twisted Hilbert spaces
No full text[EN] We provide three new examples of twisted Hilbert spaces by considering prop-erties that are "close" to Hilbert. We denote them Z(J), Z(S2) and Z(Ts2). The first space is asymptotically Hilbertian but not weak Hilbert. On the opposite side, Z(S2) and Z(Ts2) are not asymptotically Hilbertian. Moreover, the space Z(Ts2) is a HAPpy space and the technique to prove it gives a "twisted" version of a theorem of Johnson and Szankowski (Ann. of Math. 176:1987-2001, 2012). This is, we can construct a nontrivial twisted Hilbert space such that the isomorphism con-stant from its n-dimensional subspaces to ln2 grows to infinity as slowly as we wish when n -> infinity.SIMinisterio de economía, industria y competitividad ( MTM2016-76958-C2-1-P)Agencia Estatal de InvestigaciónThe first author was supported by the grant BES-2017-079901 of the project MTM2016-76958-C2-1-P. The second author was supported in part by projects MTM2016-76958-C2-1-P, PID2019-103961GB-C21 and IB16056. This is part of the thesis of first named author under the supervision of Jesús M. F. Castillo and the second named author
The Hilbert-Polya Conjecture and the Prolate Spheroidal Operator
No full textOne possible way of proving the famous and important Riemann hypothesis would be to realize the Riemann zeta zeroes as the eigenvalues of some self-adjoint operator, using self-adjointness to show that the non-trivial zeroes all lie on the critical line. This is known as the Hilbert-Polya conjecture. Interpreting such a self-adjoint operator as an observable of some quantum system, one can try to describe the Riemann zeta zeroes in physical terms, making the Hilbert-Polya conjecture an interesting border case between mathematics and physics. Major work on the Hilbert-Polya conjecture was done by Alain Connes. In his framework, the prolate spheroidal differential operator plays an important but auxiliary role. Before Connes’ work, this second-order differential operator was mainly known for its use in signal analysis, specifically in Slepian’s work on signals which are both time-limited and band-limited. In a more recent article, Connes and Moscovici show that the relation between the prolate spheroidal operator and the Riemann zeta function might be deeper than it seems. They show that a certain self-adjoint realization of the prolate spheroidal operator on the entire real line has discrete spectrum that is asymptotically similar to the squares of the Riemann zeta zeroes. This surprising discovery allows them to construct an operator which approximately solves the Hilbert-Polya conjecture. Though Connes and Moscovici’s article is wonderful and inspiring, it is tersely written. Hence, in this bachelor thesis, details have been provided to the reasoning of the article. In addition, the physical interpretations of the Riemann zeta zeroes, which support the Hilbert-Polya conjecture, have also been presented. Applied Mathematics | Applied Physic
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