• Kyungpook Mathematical Journal
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• 제56권4호
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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.

• 전자공학회논문지S
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• 제34S권2호
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• pp.94-103
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• 1997

The WCHF-FSJTC (wavelet circular harmonic function frequency selective joint transform correlator) using th wavelet transformed CHF as the reference image in FSJTC is proposed for rotation invariant pattern recognition. Since the wavelet transform has the property of feature extraction, the proposed system can have the better DC (discrimination cpability) and the higher SNR(signal to noise ratio) compared with the conventional CHF-CJTC(circular harmonic function conventional joint transform correlator). And since the structure of the proposed system is FSJTC which can eliminate auto-correlation and cross-correlation between input images, it can eliminate false alarm caused by the overlapping among correlation peaks. The used wavelet functio is the morlet function, which is proper for the reference image used in this paper. the optimal dialation parameter and oscillation frequency of the wavelet function are also achieved with varying the parameters of the wavelet function. The computer simulation shows that the proposed system has the best performance when the dilation parameter is 0.8 and the oscillation frequency is 0.48.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.519-527
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• 2007

In this paper, we establish a theorem wherein we have obtained the image of modified H-transform under the fractional integral operator involving Foxs H-function. Three corollaries of this theorem have also been derived. Further, we obtain one interesting integral by the application of the third corollary. The importance of above findings lies in the fact that our main theorem involves Fox H-function which is very general in nature. The result obtained earlier by Tariq (1998) is a special case of our main findings.

• 대한수학회보
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• 제41권1호
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• pp.73-93
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• 2004

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

• 대한수학회논문집
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• 제21권3호
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• pp.419-428
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• 2006

The Berezin transform is the analogue of the Poisson transform in the Bergman spaces. Dyakonov characterize the holomorphic weighted Lipschitz function in the unit disk in terms of the Possion integral. In this paper, we characterize the harmonic weighted Lispchitz function in terms of the Berezin transform instead of the Poisson integral.

• 정보처리학회논문지D
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• 제14D권2호
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• pp.169-180
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• 2007

본 논문은 함수 변환(Function Transform)과 FFT(Fast Fourier Transform)를 사용하는 새로운 XML 문서 클리스터링 기법에 대하여 논한다. 본 문서 클러스터링 기법은 조정자 없이 점진적으로 수행된다. XML 문서는 엘리먼트의 계층적인 구조에 기반하여 이산 함수로 변환된다. 이산 함수는 FFT를 사용하여 벡터로 변환된다. 문서를 나타내는 벡터는 가중치 유클리디안 거리 메트릭을 사용하여 비교된다. 비교 결과가 미리 정의된 값보다 작을 때에는 비교되는 두 개의 문서는 구조적으로 비슷한 것으로 간주되어 동일한 그룹으로 분류된다. XML 문서 클리스터링은 XML 문서의 저장과 검색에 유용하게 사용될 수 있다. 800개의 합서 문서와 520개의 실제 문서를 사용하여 실험하였다. 실험 결과는 함수변환과 FFT는 XML 문서를 엘리먼트의 구조를 기반으로 하여 점진적으로 조정자 없이 효과적으로 분류하는 것을 보여주었다.

• 대한수학회논문집
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• 제36권4호
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• pp.705-714
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• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• East Asian mathematical journal
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• 제35권1호
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• pp.23-30
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• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.

• 대한수학회지
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• 제49권5호
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• pp.1065-1082
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• 2012

In this paper we first investigate the existence of the generalized Fourier-Feynman transform of the functional F given by $$F(x)={\hat{\nu}}((e_1,x)^{\sim},{\ldots},(e_n,x)^{\sim})$$, where $(e,x)^{\sim}$ denotes the Paley-Wiener-Zygmund stochastic integral with $x$ in a very general function space $C_{a,b}[0,T]$ and $\hat{\nu}$ is the Fourier transform of complex measure ${\nu}$ on $B({\mathbb{R}}^n)$ with finite total variation. We then define two sequential transforms. Finally, we establish that the one is to identify the generalized Fourier-Feynman transform and the another transform acts like an inverse generalized Fourier-Feynman transform.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.