• 대한수학회보
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• 제48권2호
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• pp.291-302
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• 2011

We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification $\cal{B}_C$ of an abstract Wiener space ($\cal{H}$, $\cal{B}$, ${\nu}$). Secondly, we introduce a new class of convolution products of functionals defined on $\cal{B}_C$ and study several properties of the convolutions. Then we study various relations among the first variation the convolutions, and the generalized Fourier-Gauss transforms.

• Interaction and multiscale mechanics
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• 제3권1호
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• pp.81-94
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• 2010

The steady state response of a rotating generalized thermoelastic solid to a moving point load has been investigated. The transformed components of displacement, force stress and temperature distribution are obtained by using Fourier transformation. These components are then inverted and the results are obtained in the physical domain by applying a numerical inversion method. The numerical results are presented graphically for a particular model. A particular result is also deduced from the present investigation.

• 한국음향학회지
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• 제35권1호
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• pp.8-15
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• 2016

Fractional 푸리에 변환(Fractional Fourier Transform : FrFT)은 기존의 푸리에 변환의 일반화된 형태로서, 변환차수 ${\alpha}$에 따라 임의의 시간-주파수 영역에서의 신호해석이 가능하다. FrFT는 특히 LFM(Linear Frequency Modulation) 신호의 분석에 있어 잡음에 강한 특성으로 인해 많은 장점을 가진다. 본 논문에서는 능동소나에서 표적에 맞고 반향된 수신신호의 FrFT 스펙트럼으로부터 표적과의 거리를 추정하는 새로운 방법을 제안하였다. 합성한 표적 신호를 통해 제안한 방법의 타당성을 검증하였으며, 실제 수중 실험을 통해 얻은 잡음 및 잔향 환경에서의 신호에서도 신뢰성 있는 표적과의 거리 추정이 가능함을 확인하였다.

• 대한수학회논문집
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• 제25권3호
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• pp.391-404
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• 2010

The well-known characterizations of the Schwartz space of rapidly decreasing functions is extended to new algebras of rapidly decreasing generalized functions.

• Structural Engineering and Mechanics
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• 제28권1호
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• pp.19-38
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• 2008

A general solution to the field equations of homogeneous isotropic generalized thermoelastic diffusion with two relaxation times (Green and Lindsay theory) has been obtained using the Fourier transform. Assuming the disturbances to be harmonically time.dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed loads have been considered to show the utility of the solution obtained. The transformed components of displacement, stress, temperature distribution and chemical potential distribution are inverted numerically, using a numerical inversion technique. Effect of diffusion on the resulting expressions have been depicted graphically for Green and Lindsay (G-L) and coupled (C-T) theories of thermoelasticity.

• Structural Engineering and Mechanics
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• 제29권6호
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• pp.673-687
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• 2008

In this paper, a thermo-viscoelastic problem in an infinite isotropic medium in two dimensions in the presence of a point heat source is considered. The fundamental equations of the problems of generalized thermoelasticity including heat sources in a thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace-Fourier transform domain for a two dimensional problem. These equations have been solved by the eigenvalue approach. The results have been compared to those available in the existing literature. The graphs have been drawn for different cases.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.825-834
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• 2013

In this paper, we study the Yeh convolution of white noise functionals. We first introduce the notion of Yeh convolution of test white noise functionals and prove a dual property of the Yeh convolution. By applying the dual object of the Yeh convolution, we study the Yeh convolution of generalized white noise functionals, which is a non-trivial extension. Finally, we study relations between the Yeh convolution and Fourier-Gauss, Fourier-Mehler transform.

• 대한수학회지
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• 제25권1호
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• pp.133-148
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• 1988

• 대한수학회보
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• 제48권5호
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• pp.1003-1014
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• 2011

Motivated by the convolution product of white noise functionals, we introduce a new notion of convolution products of white noise operators. Then we study several interesting relations between the convolution products and the quantum generalized Fourier-Mehler transforms, and study a quantum-classical correspondence.

• Kyungpook Mathematical Journal
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• 제63권3호
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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.