Bicomplex Analogs of Segal–Bargmann and Fractional Fourier Transforms

Ghanmi, Allal; Zine, Khalil

doi:10.1007/s00006-019-0993-9

Cited by 8 publications

(5 citation statements)

References 25 publications

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“…Thus the concrete description of analytic properties of these transforms are obtained. It gives rise to special generalization of the bicomplex Bargmann space studied in [9]. One of the advantage of this setting is to work simultaneously with two models of the polyanalytic Bargmann space F 2,σ n (C τ ), the first one is focused on e + and the other on e − .…”

Section: Discussionmentioning

confidence: 99%

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On bicomplex Fourier–Wigner transforms

Gourari

Ghanmi

Zine

2020

Int. J. Wavelets Multiresolut Inf. Process.

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We consider the 1-and 2-d bicomplex analogs of the classical Fourier-Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex-polyanalytic functional spaces are discussed. Particular case of special window is also considered. An orthogonal basis for the space of bicomplex-valued square integrable functions on the bicomplex numbers is constructed by means of the polyanalytic complex Hermite functions.2010 Mathematics Subject Classification. Primary 30G35; 44A15; Secondary 32A17.

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Section: Discussionmentioning

confidence: 99%

“…We will rely mostly on the notations and basic tools as given in [9] and relevant to bicomplex numbers T, bicomplex holomorphic functions and bicomplex Hilbert spaces, For further detail, we can refer to [12,15,9] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On bicomplex Fourier–Wigner transforms

Gourari

Ghanmi

Zine

2020

Int. J. Wavelets Multiresolut Inf. Process.

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“…The bicomplex Fourier transform for functions of bicomplex variables is studied in [2,3,9]. The standard bicomplex Fourier transform is defined as…”

Section: Bicomplex Fourier Transformsmentioning

confidence: 99%

Exploring Academic Dishonesty Among University Students: University of Jammu, India

Kumar¹,

Dabgotra²

2023

Artificial Intelligence and Communication Technologies

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Over the years, academic cheating continues to be an endemic issue that has always been a threat to academic honesty and social values. Academic dishonesty among the students is a perplexing phenomenon, that exists in every stage of our education system, especially in colleges and universities. College and university administrators admit that academic dishonesty is an issue on campus but they often lack in preparing effective policies and procedures to monitor it and to deal with it. In addition, indecisive perceptions regarding academic dishonesty has adverse effects on paradoxical situation of education. The current study provides details about the causes that motivate students to cheat and describes the different forms of cheating practices performed by the students. The purpose of this study is to define the students of University of Jammu what is meant by academic cheating, to determine the factors associated with cheating behaviour and to classify of the students according to their cheating behaviour. From the current study, the main reasons due to which students go for cheating are not knowing/understanding the study material, performance pressure, inadequate exam preparations, etc. Also, around 42%, 6% and 52% of the respondents are found to be occasional, persistent and instantaneous cheaters, respectively. We suggest that students must understand that cheating is wrong not only for the society but also for their own knowledge because by indulging in cheating students prevent them from learning what they are studying and hence, deteriorate the intellectual human resource of the country.

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“…Cerejeiras et al [17] reconstructed a bicomplex sparse signal with high probability from a reduced number of bicomplex random samples. Ghanmi and Zine [4] introduced bicomplex Segal-Bargmann and fractional Fourier transforms. Double Laplace transform proposed by Van der Pol [31] and applied by Humbert [18] in the study of hypergeometric functions; by Jaeger [12] to solve boundary value problems in heat conduction.…”

Section: Introductionmentioning

confidence: 99%

Triple Laplace Transform in Bicomplex Space with Application

Goswami¹,

Jha²

2020

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In this article, we investigate bicomplex triple Laplace transform in the framework of bicomplexified frequency domain with Region of Convergence (ROC), which is generalization of complex triple Laplace transform. Bicomplex numbers are pairs of complex numbers with commutative ring with unity and zero-divisors, which describe physical interpretation in four dimensional space and provide large class of frequency domain. Also, we derive some basic properties and inversion theorem of triple Laplace transform in bicomplex space. In this technique, we use idempotent representation methodology of bicomplex numbers, which play vital role in proving our results. Consequently, the obtained results can be highly applicable in the fields of Quantum Mechanics, Signal Processing, Electric Circuit Theory, Control Engineering, and solving differential equations. Application of bicomplex triple Laplace transform has been discussed in finding the solution of third-order partial differential equation of bicomplex-valued function.

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Bicomplex Analogs of Segal–Bargmann and Fractional Fourier Transforms

Cited by 8 publications

References 25 publications

On bicomplex Fourier–Wigner transforms

On bicomplex Fourier–Wigner transforms

Exploring Academic Dishonesty Among University Students: University of Jammu, India

Triple Laplace Transform in Bicomplex Space with Application

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