• 대한수학회논문집
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• 제24권3호
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• pp.397-413
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• 2009

In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.

• 대한수학회지
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• 제38권1호
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• pp.61-76
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• 2001

In this paper we define the concept of a conditional Fourier-Feynman transform and a conditional convolution product and obtain several interesting relationships between them. In particular we show that the conditional transform of the conditional convolution product is the product of conditional transforms, and that the conditional convolution product of conditional transforms is the conditional transform of the product of the functionals.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.43-63
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• 2014

The range spaces of Fourier cosine and sine transforms on $L^1$([0, ${\infty}$)) are characterized. Using Fourier cosine and sine type convolutions, Fourier cosine and sine transformable Boehmian spaces have been constructed, which properly contain $L^1$([0, ${\infty}$)). The Fourier cosine and sine transforms are extended to these Boehmian spaces consistently and their properties are established.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.335-347
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• 2017

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.649-671
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• 2020

In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on ℝd, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on ℝd in the W-invariant case.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.667-691
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• 2016

This study focuses on the damage detection of defect types in plate structures based on wavelet transform (WT) and curvelet transform (CT). In particular, for damage detection of structures these transforms have been developed since the last few years. In recent years, the CT approach has been also introduced in an attempt to overcome inherent limitations of traditional multi-scale representations such as wavelets. In this study, the performance of CT is compared with WT in order to demonstrate the capability of WT and CT in detection of defect types in plate structures. To achieve this purpose, the damage detection of defect types through defect shape in rectangular plate is investigated. By using the first mode shape of plate structure and the distribution of the coefficients of the transforms, the damage existence, the defect location and the approximate shape of defect are detected. Moreover, the accuracy and performance generality of the transforms are verified through using experimental modal data of a plate.

• 호남수학학술지
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• 제34권4호
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• pp.505-512
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• 2012

In this paper, we give some properties on submodule transforms.

• 충청수학회지
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• 제35권3호
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• pp.269-275
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• 2022

In this note, we verify that the bounded shadowing property and quasi-hyperbolicity of bounded linear operators on Hilbert spaces are preserved under Aluthge transforms.

• 충청수학회지
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• 제23권1호
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• pp.1-10
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• 2010

In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.