scholarly journals Relationships among the First Variation, the Convolution Product, and the Fourier-Feynman Transform

1998 ◽  
Vol 28 (4) ◽  
pp. 1447-1468 ◽  
Author(s):  
Chull Park ◽  
David Skoug ◽  
David Storvick
Keyword(s):  
Convolution Product ◽  
First Variation ◽  
The First Variation

scholarly journals Integral transforms, convolution products, and first variations

2004 ◽  
Vol 2004 (11) ◽  
pp. 579-598 ◽  
Author(s):  
Bong Jin Kim ◽  
Byoung Soo Kim ◽  
David Skoug
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Continuous Functions ◽  
Convolution Product ◽  
First Variation ◽  
Alpha Beta ◽  
Convolution Products ◽  
The First Variation ◽  
Complex Valued

We establish the various relationships that exist among the integral transformℱα,βF, the convolution product(F∗G)α, and the first variationδFfor a class of functionals defined onK[0,T], the space of complex-valued continuous functions on[0,T]which vanish at zero.

scholarly journals Relationships among transforms, convolutions, and first variations

1999 ◽  
Vol 22 (1) ◽  
pp. 191-204 ◽  
Author(s):  
Jeong Gyoo Kim ◽  
Jung Won Ko ◽  
Chull Park ◽  
David Skoug
Keyword(s):  
Stochastic Integral ◽  
Wiener Space ◽  
Convolution Product ◽  
First Variation ◽  
The First Variation

In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionalsFon Wiener space of the formF(x)=f(〈α1,x〉,…,〈αn,x〉),                                                      (*)where〈αj,x〉denotes the Paley-Wiener-Zygmund stochastic integral∫0Tαj(t)dx(t).

scholarly journals Conditional integral transforms with related topics on function space

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1151-1162 ◽  
Author(s):  
Hyun Chung ◽  
Jae Choi ◽  
Seung Chang
Keyword(s):  
Function Space ◽  
Integral Transform ◽  
Integral Transforms ◽  
Convolution Product ◽  
First Variation ◽  
Convolution Products ◽  
The First Variation

In this paper we study the conditional integral transform, the conditional convolution product and the first variation of functionals on function space. For our research, we modify the class S? of functionals introduced in [7]. We then give the existences of the conditional integral transform, the conditional convolution product and the first variation for functionals in S?. Finally, we give various relationships and formulas among conditional integral transforms, conditional convolution products and first variations of functionals in S?.

scholarly journals Relationships of convolution products, generalized transforms, and the first variation on function space

2002 ◽  
Vol 29 (10) ◽  
pp. 591-608 ◽  
Author(s):  
Seung Jun Chang ◽  
Jae Gil Choi
Keyword(s):  
Brownian Motion ◽  
Banach Algebra ◽  
Function Space ◽  
Standard Wiener Process ◽  
Convolution Product ◽  
Brownian Motion Process ◽  
First Variation ◽  
Motion Process ◽  
Generalized Brownian Motion Process ◽  
The First Variation

We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier-Feynman transform, and the convolution product for functionals on function space that belong to a Banach algebraS(Lab[0,T]). These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.

scholarly journals Existence Results for the Conformal Dirac–Einstein System

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chiara Guidi ◽  
Ali Maalaoui ◽  
Vittorio Martino
Keyword(s):  
Perturbation Methods ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Existence Results ◽  
First Variation ◽  
The First Variation

AbstractWe consider the coupled system given by the first variation of the conformal Dirac–Einstein functional. We will show existence of solutions by means of perturbation methods.

scholarly journals On $L_1$-biharmonic timelike hypersurfaces in pseudo-Euclidean space $E_1^4$

2020 ◽  
Vol 51 (4) ◽  
pp. 313-332
Author(s):  
Firooz Pashaie
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Principal Curvatures ◽  
First Variation ◽  
Chen’S Conjecture ◽  
The First Variation ◽  
Linearized Operator ◽  
Euclidean Submanifolds

A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3\rightarrow\E_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.

scholarly journals On solving the plateau problem in parametric form

1983 ◽  
Vol 6 (2) ◽  
pp. 341-361
Author(s):  
Baruch cahlon ◽  
Alan D. Solomon ◽  
Louis J. Nachman
Keyword(s):  
Minimal Surface ◽  
Numerical Method ◽  
Minimal Surfaces ◽  
Plateau Problem ◽  
Parametric Form ◽  
First Variation ◽  
Plateau’S Problem ◽  
Numerical Example ◽  
Plateau's Problem ◽  
The First Variation

This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.

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