Almost Periodic Oscillations and Waves

Corduneanu, C.

doi:10.1007/978-0-387-09819-7

Cited by 160 publications

(152 citation statements)

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“…The vector (9) will be used to denote an process composed of the distinct poles . The multiplicity of a pole is represented by the number following it in the parameter vector.…”

Section: A the Vector Of Parametersmentioning

confidence: 99%

“…Of particular interest is the fact that uniform samples of almost periodic functions lie in the normed space of almost periodic sequences (cf. ( [9], Proposition 3.35) and Appendix A), and we exploit this fact to verify uniqueness. (25) Note that, in this definition, we are free to choose any integer , and the limit will be independent of this choice.…”

Section: B the Autocorrelation Functionmentioning

confidence: 99%

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On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

Kirshner

Unser

Ward

2014

IEEE Trans. Signal Process.

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Abstract-In this work, we investigate the relationship between continuous-time autoregressive (AR) models and their sampled version. We consider uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the model order is assumed to be known. We achieve this by removing a set of measure zero from the collection of all AR models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions. We provide necessary and sufficient conditions for uniqueness of general AR models, and we demonstrate the usefulness of this result by considering particular examples. We further exploit our theory and introduce an estimation algorithm that recovers continuous-time AR parameters from sampled data, regardless of the sampling interval. We demonstrate the usefulness of our algorithm for various Gaussian and non-Gaussian AR processes.

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“…The vector (9) will be used to denote an process composed of the distinct poles . The multiplicity of a pole is represented by the number following it in the parameter vector.…”

Section: A the Vector Of Parametersmentioning

confidence: 99%

Section: B the Autocorrelation Functionmentioning

confidence: 99%

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

Kirshner

Unser

Ward

2014

IEEE Trans. Signal Process.

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“…functions (see [4][5][6][7][8][9][10][11][12]) and a.p. sequences (see [7,8,[11][12][13]). As the fact that a.p.…”

Section: Introductionmentioning

confidence: 99%

“…functions on time scales to a.p. functions on R. In [7,8], Corduneanu presented that the existence of a.p. sequence {x n } is equivalent to the existence of an a.p.…”

Section: Introductionmentioning

confidence: 99%

On the relationship of C m $C^{m}$ -almost periodicity on R $\mathbb {R}$ and time scales

Wang

2018

Adv Differ Equ

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“…The principal objective of this article is to extend the results of [19] to the space of asymptotically almost periodic sequences with relatively compact ranges denoted by AAP r 0 (Z + , ∆). For the periodic and almost periodic sequences, we refer the reader to [3,8] and the references cited there.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of discrete semigroups of bounded linear operators over Banach spaces

Tang¹,

Zada²,

Khalid³

et al. 2017

J. Math. Computer Sci.

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Assume that ϑ j is the solution of the nonhomogeneous Cauchy problemwhere ρ(1) is the algebraic generator of the discrete semigroup T = {ρ(j) : j ∈ Z + } acting on a complex Banach space ∆. Suppose further that AAP r 0 (Z + , ∆) is the space of asymptotically almost periodic sequences with relatively compact ranges. We prove that the system u j+1 = ρ(1)u j is uniformly exponentially stable if and only if for each f ∈ AAP r 0 (Z + , ∆) the solution ϑ j ∈ AAP r 0 (Z + , ∆).

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Almost Periodic Oscillations and Waves

Cited by 160 publications

References 0 publications

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

On the relationship of C m $C^{m}$ -almost periodicity on R $\mathbb {R}$ and time scales

Asymptotic behavior of discrete semigroups of bounded linear operators over Banach spaces

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