• Nonlinear Functional Analysis and Applications
• /
• 제28권4호
• /
• pp.1069-1086
• /
• 2023

The natural transform is represented by two (p, q)-analogues, and their comparative characteristics are established. To resolve some (p, q)-difference and functional equations, applications are carried out.

• Kyungpook Mathematical Journal
• /
• 제49권1호
• /
• pp.155-166
• /
• 2009

We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform $\hat{F}_{{\alpha},{\beta}}F(x)$ which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in $L_2(C_0[0,T])$.

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

• 대한수학회논문집
• /
• 제19권1호
• /
• pp.93-111
• /
• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• Nonlinear Functional Analysis and Applications
• /
• 제26권1호
• /
• pp.105-115
• /
• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• 대한수학회보
• /
• 제49권3호
• /
• pp.609-619
• /
• 2012

In this paper we define the Fourier-type functionals via the Fourier transform on Wiener space. We investigate some properties of the Fourier-type functionals. Finally, we establish integral transform of the Fourier-type functionals which also can be expressed by other Fourier-type functionals.

• East Asian mathematical journal
• /
• 제29권5호
• /
• pp.467-479
• /
• 2013

We develop a Fourier-Feynman theory for Fourier-type functionals ${\Delta}^kF$ and $\widehat{{\Delta}^kF}$ on Wiener space. We show that Fourier-Feynman transform and convolution of Fourier-type functionals exist. We also show that the Fourier-Feynman transform of the convolution product of Fourier-type functionals is a product of Fourier-Feynman transforms of each functionals.

• ETRI Journal
• /
• 제31권5호
• /
• pp.628-630
• /
• 2009

Recently, Ratha and others proposed a cancelable biometrics scheme which transforms an original fingerprint template into a new one using a noninvertible transformation. However, we show that the original template is recovered by a dictionary attack if two transformed templates originating from it are revealed. In our attack, we simulate the transformation and construct a set of possible pre-images for each transformed template. Then, we find the correct pre-image by computing the intersection of these sets. We present an algorithm implementing this idea as well as successful experimental results.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권4호
• /
• pp.281-296
• /
• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Korean Journal of Mathematics
• /
• 제6권1호
• /
• pp.47-66
• /
• 1998

In this paper, we introduce an $L_p$ analytic Fourier-Feynman transformation, show the existence of the $L_p$ analytic Fourier-Feynman transforms for a certain class of cylinder functionals on an abstract Wiener space, and investigate its interesting properties. Moreover, we define a convolution product for two functionals on the abstract Wiener space and establish the relationships between the Fourier-Feynman transform for the convolution product of two cylinder functionals and the Fourier-Feynman transform for each functional.