Search results for "42C40"

showing 3 items of 3 documents

Gabor systems and almost periodic functions

2017

Abstract Inspired by results of Kim and Ron, given a Gabor frame in L 2 ( R ) , we determine a non-countable generalized frame for the non-separable space AP 2 ( R ) of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of AP 2 ( R ) are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.

Almost periodic functionApplied Mathematics010102 general mathematicsAlmost-periodic functions010103 numerical & computational mathematicsGabor frame01 natural sciencesLinear subspaceFunctional Analysis (math.FA)Separable spaceCombinatoricsMathematics - Functional AnalysisFramesNorm (mathematics)42C40 42C15 42A75FOS: MathematicsAP-framesCountable set0101 mathematicsGabor systemsMathematicsAlmost-periodic functions; AP-frames; Frames; Gabor systems; Applied Mathematics
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A wavelet-based tool for studying non-periodicity

2010

This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map.

Dynamical systems theoryFOS: Physical sciencesLyapunov exponentDynamical Systems (math.DS)37D99 42C40WaveletsDynamical systemMeasure (mathematics)symbols.namesakeWaveletModelling and SimulationFOS: MathematicsApplied mathematicsMathematics - Dynamical SystemsContinuous wavelet transformMathematicsMathematical analysisNonlinear Sciences - Chaotic DynamicsNon-periodicityHénon mapNonlinear Sciences::Chaotic DynamicsComputational MathematicsComputational Theory and MathematicsModeling and SimulationsymbolsLogistic mapChaotic Dynamics (nlin.CD)Chaotic dynamical systems
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Quantifying non-periodicity of non-stationary time series through wavelets

2019

In this paper, we introduce a new wavelet tool for studying the degree of non-periodicity of time series that is based on some recently defined tools, such as the \textit{windowed scalogram} and the \textit{scale index}. It is especially appropriate for non-stationary time series whose characteristics change over time and so, it can be applied to a wide variety of disciplines. In addition, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of …

FOS: MathematicsFOS: Physical sciencesDynamical Systems (math.DS)37D99 42C40Chaotic Dynamics (nlin.CD)Mathematics - Dynamical SystemsNonlinear Sciences - Chaotic Dynamics
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