• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.425-435
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• 2023

The classical Hardy Theorem on R states that a function f and its Fourier transform cannot be simultaneously very small; this fact was generalized by Miyachi in terms of L¹ + L^∞ and log⁺-functions. In this paper, we consider the k-Hankel transform, which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl's theory. We study Miyachi's theorem for the k-Hankel transform on ℝ^d.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1607-1619
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• 2015

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.521-535
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• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.827-832
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• 2013

In this paper we apply the Catalan transform to the ${\kappa}$-Fibonacci sequence finding different integer sequences, some of which are indexed in OEIS and others not. After we apply the Hankel transform to the Catalan transform of the ${\kappa}$-Fibonacci sequence and obtain an unusual property.

• Geophysics and Geophysical Exploration
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• v.14 no.3
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• pp.185-190
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• 2011

In marine controlled-source electromagnetic (CSEM) modeling, it may be difficult to evaluate primary fields accurately using conventional linear filters because they decay very rapidly with distance. However, since there exists a closed-form solution to the Hankel transform in TM mode for a homogeneous half space, we can assess the accuracy of linear filters for evaluating the Hankel transform. As a result, only nine out of 36 source-receiver pairs show that EM fields decrease linearly in semi-log scale with an increase of source-receiver distance, while EM fields are either 0 or not reduced significantly due to an effect of the air layer. There also exist closed-form solutions for the nine pairs, and the others can be evaluated accurately with a relatively short filter. This paper proposes a method which uses closed-form solutions for TM-mode Hankel transforms and a filter with 61 coefficients for TE-mode ones.

• Geomechanics and Engineering
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• v.19 no.1
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• pp.29-36
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• 2019

The present research deals with the deformation in transversely isotropic thin circular thermoelastic rotating plate due to time-harmonic sources. Frequency effect in the presence of rotation and two temperature is studied under thermally insulated as well as isothermal boundaries. The Hankel transform technique is used to find a solution to the problem. The displacement components, stress components, and conductive temperature distribution with the radial distance are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. Some specific cases are also figured out from the current research.

• Economic and Environmental Geology
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• v.20 no.2
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• pp.119-123
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• 1987

Hankel transform of order 0 can be represented by a combination of Abel transform and Fourier transform. This Abel-Fourier method can offer computational advantages over a conventional digital linear filter method through the uses of a rapid Abel transform with shift variant recursive filter and of a fast Fourier transform. The Abel-Fourier method, however, is generally less accurate than a well-designed digital linear filter method. In geoelectrical applications, the digital linear filter method seems to be more flexible than the Abel-Fourier method.

• Kyungpook Mathematical Journal
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• v.9 no.1_2
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• pp.31-36
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• 1969

• Kyungpook Mathematical Journal
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• v.9 no.1_2
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• pp.47-52
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• 1969

• Kyungpook Mathematical Journal
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• v.25 no.1
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• pp.83-92
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• 1985