• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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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.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.139-168
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• 2016

In this work, we rst introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions f(z) in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions f'(z) and $f^{\prime}_m(z)$ are determined by using the coecient estimates.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.183-198
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• 1999

Let $\mathcal{F}(B)$ be the Fresnel class on an abstract Wiener space (B, H, ${\omega}$) which consists of functionals F of the form : $$F(x)={\int}_H\;{\exp}\{i(h,x)^{\sim}\}df(h),\;x{\in}B$$ where $({\cdot}{\cdot})^{\sim}$ is a stochastic inner product between H and B, and $f$ is in $\mathcal{M}(H)$, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an $L_p$ analytic Fourier-Feynman transform ($1{\leq}p{\leq}2$) and a convolution product on $\mathcal{F}(B)$ and verify the existence of the $L_p$ analytic Fourier-Feynman transforms for functionls in $\mathcal{F}(B)$. Moreover, we verify that the Fresnel class $\mathcal{F}(B)$ is closed under the $L_p$ analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the $n$-repeated $L_p$ analytic Fourier-Feynman transform on $\mathcal{F}(B)$. Finally, we show that several results in [9] come from our results in Section 3.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1169-1177
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• 2016

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

• Kyungpook Mathematical Journal
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• v.19 no.1
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• pp.119-125
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• 1979

In the present paper we study a new integral transform whose kernel involves the product of two H-functions of two complex variables. Next, we establish an inversion formula for this new transform. On account of very general nature of its kernel, several other integral transforms studies earlier by many research workers viz., Bose (1952), Mukherji (1962), Nigam (1963), Rathie (1965), Singh (1969), Mittal & Goel (1973), and Gupta, Garg & Kalla (1975), follow as its particular cases.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1299-1309
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• 2021

Demeter [1] and Kuk and Lee [5] proved the unboundedness of the trilinear Hilbert transforms H_a,b,c under the critical index 1/2 for some parameters a, b and c. We show the unboundedness of H_a,b,c for any parameters.

• Journal of Broadcast Engineering
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• v.17 no.6
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• pp.1110-1113
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• 2012

Various image interpolation methods have been proposed to increase the resolution of images and accuracy of motion estimation of video, and the interpolation filters are used in H.264/AVC and HEVC standards. In this paper, we propose an efficient image interpolation method using lapped transforms. The relation between the resizing and interpolation of images is used in the proposed method, and the complexity is significantly reduced, while the performance of the proposed method is almost the same as conventional methods.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1984.04a
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• pp.13-17
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• 1984

A hybrid version of the Hadamard and center Line Symmetric Haar Transform called H-CLSH is defined and developed. Efficient algorithms for fast computation of the H-CLSH and its inverse are developed. The H-CLSH is applied to digital signal and image processing and its utility and image processing and its utility and effectiveness are compared with Hadamard-Haar discrete transforms on the basis of some standard performance criteria.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.60.1-60
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• 2002

. an output feedback stabilizing controller for non-minimum phase nonlinear systems . Assumption 1 : the Jacobi linearization of the given nonlinear linear system is controllable . Assumption 2: an appropriate transformation which transforms the zero dynamics into a special form . Assumption 3: the system satisfies the observability rank condition . Augmentation of systems by augmented by a chain of integrators