• Korean Journal of Mathematics
• /
• v.27 no.2
• /
• pp.487-503
• /
• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.281-290
• /
• 2007

We deal with Bergman functions defined on the half-plane. We study integral operators, and some relationship between Berezin transforms and Toeplitz operators, and also show that some Berezin transforms are Mobius invariant.

• Communications of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.779-790
• /
• 2016

Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.2
• /
• pp.231-246
• /
• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

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

• 한국데이터정보과학회:학술대회논문집
• /
• 2005.10a
• /
• pp.171-176
• /
• 2005

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. We build the Kolmogorov's backward differential equation and solve it to obtain the Laplace transforms of the first exit times for this dam.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.123-135
• /
• 2016

In this article, we introduce the transforms of Pythagorean and quadratic means of weighted shifts. We then explore how the transforms of weighted shifts behaves, in comparison with the Aluthge transform.

• Honam Mathematical Journal
• /
• v.35 no.1
• /
• pp.51-71
• /
• 2013

In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.591-601
• /
• 2016

Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.16 no.6
• /
• pp.1273-1278
• /
• 2012

In this paper, we introduce modified integer transforms for lossless image compression and evaluate their performances for two-dimensional transforms. The two-dimensional extensions of the modified integer transforms show different performances in terms of coding efficiency and computational complexity. Thus, we measure performances for two-dimensional separable transforms and a two-dimensional non-separable transform. The separable modified integer transform used in H.264, the modified integer transform using the lifting scheme, and the non-separable transform in JPEG XR are evaluated in this paper. Also, experiments and their results are given. The experimental results indicate that the modified integer transform using the lifting scheme shows the best performance in terms of compression efficiency.