• 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.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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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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• v.47 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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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.

• The KIPS Transactions:PartD
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• v.14D no.2
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• pp.169-180
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• 2007

This paper discusses a new unsupervised XML document clustering technique based on the function transform and FFT(Fast Fourier Transform). An XML document is transformed into a discrete function based on the hierarchical nesting structure of the elements. The discrete function is, then, transformed into vectors using FFT. The vectors of two documents are compared using a weighted Euclidean distance metric. If the comparison is lower than the pre specified threshold, the two documents are considered similar in the structure and are grouped into the same cluster. XML clustering can be useful for the storage and searching of XML documents. The experiments were conducted with 800 synthetic documents and also with 520 real documents. The experiments showed that the function transform and FFT are effective for the incremental and unsupervised clustering of XML documents similar in structure.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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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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• v.35 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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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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• v.29 no.1
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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.