Fourier Analysis of Almost Periodic Functions

Corduneanu, C.

doi:10.1007/978-0-387-09819-7_4

Cited by 37 publications

(58 citation statements)

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“…Then by [6,Theorem 8], any bounded solution of the previous system is necessarily almost periodic on Z. And by the construction above this produces an almost periodic sequence on Z + .…”

Section: X(t + 1) = Ax(t) + G(t)mentioning

confidence: 95%

Population models in almost periodic environments

Diagana

Elaydi

Yakubu

2007

Journal of Difference Equations and Applications

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Abstract. We establish the basic theory of almost periodic sequences on Z + . Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.

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“…Then by [6,Theorem 8], any bounded solution of the previous system is necessarily almost periodic on Z. And by the construction above this produces an almost periodic sequence on Z + .…”

Section: X(t + 1) = Ax(t) + G(t)mentioning

confidence: 95%

Population models in almost periodic environments

Diagana

Elaydi

Yakubu

2007

Journal of Difference Equations and Applications

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“…Since d(t) and x(t) are jointly almost-cyclostationary by assumption, their autoand cross-correlation functions are almost-periodic functions of time, and therefore they can be expanded as a generalized Fourier series (Corduneanu, 1968;Gardner, 1986):…”

Section: Let D(t) Be the Estimate Of D(t) From X(t) Obtained Throughmentioning

confidence: 99%

Adaptive-FRESH Filtering

Yeste-Ojeda¹,

Grajal²

2011

Adaptive Filtering

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“…Clearly, P is nonnegative Also, ||Pf || 1 = ||f || 1 . To see this, we need to compute ||Pf || 1 . By interchanging the integral signs, we can write:…”

Section: Lemma 43 the Following Holdsmentioning

confidence: 99%

On the stochastic Beverton–Holt equation with survival rates

Bezandry

Diagana

Elaydi

2008

Journal of Difference Equations and Applications

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Abstract. The paper studies a Beverton-Holt difference equation, in which both the recruitment function and the survival rate vary randomly. It is then shown that there is a unique invariant density, which is asymptotically stable. Moreover, a basic theory for random mean almost periodic sequence on Z + is given. Then, some sufficient conditions for the existence of a mean almost periodic solution to the stochastic Beverton-Holt equation are given.

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Fourier Analysis of Almost Periodic Functions

Cited by 37 publications

References 0 publications

Population models in almost periodic environments

Population models in almost periodic environments

Adaptive-FRESH Filtering

On the stochastic Beverton–Holt equation with survival rates

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