• Kyungpook Mathematical Journal
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• v.54 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.791-809
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• 2016

By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.485-494
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• 2021

In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

• The Transactions of the Korea Information Processing Society
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• v.6 no.4
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• pp.1112-1119
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• 1999

Digital watermarking is to embed imperceptible mark into image, video, audio and text data to prevent the illegal copy of multimedia data, arbitrary modification, and also illegal sales of the copes without agreement of copyright ownership. The DCT(discrete Cosine Transforms) transforms of original image is conducted in this research and these DCT coefficients are expanded by Fourier series expansion algorithm. In order to embed the imperceptible and robust watermark, the Fourier coefficients(lower frequency coefficients) can be calculated using sine and cosine function which have a complete orthogonal basis function, and the watermark is embedded into these coefficients, In the experiment, we can show robustness with respect to image distortion such as JPEG compression, bluring and adding uniform noise. The correlation coefficient are in the range from 0.5467 to 0.9507.