Real Paley–Wiener theorems and Roe's theorem associated with the Opdam–Cherednik transform

Andersen, Nils Byrial

doi:10.1016/j.jmaa.2015.02.032

Cited by 13 publications

(7 citation statements)

References 16 publications

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“…In this section, we collect the necessary definitions and results from the harmonic analysis related to the Opdam-Cherednik transform. The main references for this section are [2,24,27,28,31]. However, we will use the same notation as in [21,29].…”

Section: Harmonic Analysis and The Opdam-cherednik Transformmentioning

confidence: 99%

“…However, without using the short-time Fourier transform, we define the localization operator using the windowed Opdam-Cherednik transform. As the harmonic analysis associated with the Opdam-Cherednik transform has known remarkable development (see [2,24,27,28,31]), the natural question to ask whether there exists the equivalent of the theory of localization operators in the framework of the Opdam-Cherednik transform. In this paper, we mainly concern the windowed Opdam-Cherednik transform under the setting of the Opdam-Cherednik transform.…”

Section: Introductionmentioning

confidence: 99%

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Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

Poria

2021

Preprint

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In this paper, we study a class of pseudodifferential operators known as timefrequency localization operators, which depend on a symbol ς and two windows functions g1 and g2. We first present some basic properties of the windowed Opdam-Cherednik transform. Then, we use modulation spaces associated with the Opdam-Cherednik transform as appropriate classes for symbols and windows, and study the boundedness and compactness of the localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten-von Neumann class.

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Section: Harmonic Analysis and The Opdam-cherednik Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

Poria

2021

Preprint

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“…In this section, we collect the necessary definitions and results from the harmonic analysis related to the Opdam-Cherednik transform. The main references for this section are [1,23,26,27,29]. However, we will use the same notation as in [21].…”

Section: Harmonic Analysis and The Opdam-cherednik Transformmentioning

confidence: 99%

“…(i) If ab > 1 4 , then f = 0 almost everywhere. (ii) If ab = 1 4 , then the function f is of the form f (x) = Ce −ax 2 , for some constant C. (iii) If ab < 1 4 , then any finite linear combination of Hermite functions satisfies these decay conditions.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty principles for the Opdam-Cherednik transform on modulation spaces

Poria

2020

Preprint

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“…, )) is a continuous function, ( ) ∈ , ⊂ , assume that ( ) is a bounded ∞ function. Based on the Paley-Wiener Theorem [39], the Fourier transform ( ) ( = ( 1 , . .…”

Section: Definition 3 Given An Arbitrary Continuous Functionmentioning

confidence: 99%

A Hybrid Forecasting Model Based on Empirical Mode Decomposition and the Cuckoo Search Algorithm: A Case Study for Power Load

Heng

Wang

Zhao

et al. 2016

Mathematical Problems in Engineering

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Power load forecasting always plays a considerable role in the management of a power system, as accurate forecasting provides a guarantee for the daily operation of the power grid. It has been widely demonstrated in forecasting that hybrid forecasts can improve forecast performance compared with individual forecasts. In this paper, a hybrid forecasting approach, comprising Empirical Mode Decomposition, CSA (Cuckoo Search Algorithm), and WNN (Wavelet Neural Network), is proposed. This approach constructs a more valid forecasting structure and more stable results than traditional ANN (Artificial Neural Network) models such as BPNN (Back Propagation Neural Network), GABPNN (Back Propagation Neural Network Optimized by Genetic Algorithm), and WNN. To evaluate the forecasting performance of the proposed model, a half-hourly power load in New South Wales of Australia is used as a case study in this paper. The experimental results demonstrate that the proposed hybrid model is not only simple but also able to satisfactorily approximate the actual power load and can be an effective tool in planning and dispatch for smart grids.

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Real Paley–Wiener theorems and Roe's theorem associated with the Opdam–Cherednik transform

Cited by 13 publications

References 16 publications

Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

Localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces

Uncertainty principles for the Opdam-Cherednik transform on modulation spaces

A Hybrid Forecasting Model Based on Empirical Mode Decomposition and the Cuckoo Search Algorithm: A Case Study for Power Load

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