• Kyungpook Mathematical Journal
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• 제54권3호
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• pp.365-374
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• 2014

In this paper, we introduce a new subclass of meromorphic functions defined in the punctured unit disc. We derive inclusion relationships, radius problem and some other interesting properties of this class are investigated.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.221-267
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• 2019

In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and $^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on ${\mathbb{R}}^d$. By using these operators we define the hypergeometric translation operator ${\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, and its dual $^t{\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, we express them in terms of the hypergeometric Fourier transform ${\mathcal{H}}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform ${\mathcal{H}}^W$. We study also the hypergeometric convolution product on W-invariant $L^p_{\mathcal{A}k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

• 대한수학회지
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• 제54권1호
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• 호남수학학술지
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• 제38권2호
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• pp.243-257
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• 2016

If we let $L(2K;n):=\sum_{s=0}^{k-1}(^{2k}_{2s+1})\sum_{m=1}^{n-1}{\sigma}_{2k-2s-1,1}(m;2){\sigma}_{2s+1,1}(n-m;2)$ with $${\sigma}_{k,l}(n;2):=\sum\limits_{{d{\mid}n}\atop{d{\equiv}l(mod2)}}d^k$$, then we get the formula of L(2u; p)L(2v; p)L(2w; p).

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• 대한수학회지
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• 제45권2호
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• pp.455-466
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• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

• 대한전자공학회논문지SD
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• 제46권7호
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• pp.29-38
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• 2009

본 연구에서는 실시간 이산웨이블릿변환을 위한 컨볼루션기반 non-cascaded 구조를 구현하고자 병렬곱셈기-중간버퍼-병렬누적기의 고성능 병렬파이프라인 연산회로를 설계하였다. 이산웨이블릿변환의 컨볼루션 곱셈연산은 필터계수의 대칭성과 업/다운 샘플링이 고려된 최적화를 통해서 1/4정도로 감소시킬 수 있으며, 화상데이터와 다수 필터계수들 간의 곱셈과정을 LUT기반의 병렬계수 DA 곱셈기 구조로 구현하면 3$\sim$5배 고속연산처리가 가능하게 된다. 또한 컨볼루션의 곱셈결과를 중간버퍼에 저장하여 누적가산 과정에서 재사용하면 전체 곱셈연산량을 1/2로 감소시켜 연산전력을 절약시킬 수 있다. 중간버퍼는 화상데이터와 필터계수들의 곱셈결과값들을 컨볼루션의 누적가산 과정을 위해 정렬시켜 저장하게 되는데, 이때 병렬누적가산기의 고속 순차검색을 위해 정렬된 병렬저장이 이루어지도록 버퍼관리 구조를 설계한다. 컨볼루션의 병렬곱셈기와 병렬누적가산기는 중간버퍼를 이용한 파이프라인을 구성하게 되는데, 파이프라인 연산처리 효율을 높이기 위해 병렬곱셈기의 연산처리 성능에 맞추어 누적가산기 및 중간버퍼의 병렬화 구조가 결정된다. 설계된 고성능 이산웨이블릿변환기의 성능을 검증하기 위해서 0.18um 라이브러리를 이용한 후반부 설계를 하였으며, 90MHz에서 SVGA(800$\sim$600)영상을 30fps로 실시간 처리함을 확인하였다.

• 응용통계연구
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• 제23권4호
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• pp.621-633
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• 2010

This paper considers a certain expense structure where a vendor of equity-linked investment product will collect its expenses continuously from the investor's account whenever the investment performance exceeds a certain threshold level. Under the Black-Scholes framework, we derive compact convolution formulas for evaluating the total expenses to be collected during the investment period by using the joint Laplace transform of the Brownian motion and its excursion time. We provide numerical examples for illustration.

• 대한수학회논문집
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• 제10권2호
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• pp.305-315
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• 1995

The class $R_{\gamma-1,p}(A,B,\alpha)$ for $-1 \leq B < A \leq 1,\gamma > (B -1)p+(A_B)(p-\alpha)/1-B$ and $0 \leq \alpha < p$ consisting of p-valently analytic functions in the open unit disc is defined with the help of convolution technique. We study containment property, integral transforms and a sufficient condition for an analytic function to be in $R_{\gamma-1,p}(A,B,\alpha)$.

• 대한수학회논문집
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• 제22권4호
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• pp.553-564
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• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.