共查询到20条相似文献，搜索用时 15 毫秒
1.
《Integral Transforms and Special Functions》2012,23(3-4):179-200
Park, Skoug and Storvick examined various relationships among the first variation, the Fourier-Feynman tranform, and the convolution product for functionals, on classical Wiener space(C o[0,1],m), which belong to some Banach algebra S.In this paper, we extend the above concepts to an abstract Wiener space(B,ν)and the first variation for functionals in the Fresnel Class F(B)which corresponds to S. Since the Fresnel class F(B)is the abstracat Wiener space setting of the Banach algebra S, our result inclued the above results as special cases 相似文献
2.
Seung Jun Chang Jae Gil Choi David Skoug 《Transactions of the American Mathematical Society》2003,355(7):2925-2948
In an upcoming paper, 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 establish several integration by parts formulas involving generalized Feynman integrals, generalized Fourier-Feynman transforms, and the first variation of functionals of the form where denotes the Paley-Wiener-Zygmund stochastic integral .
3.
《Integral Transforms and Special Functions》2012,23(2):148-162
The aim of this paper is to introduce the analytic bilateral Laplace-Feynman transform for cylinder functionals on Wiener space. Using our translation theorem for the Wiener integral, we also examine the relationship between the bilateral Laplace-Feynman transform and the Fourier-Feynman transform. 相似文献
4.
Using Fourier transform techniques, we establish inequalities for integrals of the form
We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications. 相似文献
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7.
《Integral Transforms and Special Functions》2012,23(1):65-77
In this paper we define a modified analytic function space Fourier-Feynman transform to explain some physical phenomenon. We then establish various relationships involving the modified analytic function space Fourier-Feynman transform with related topics. Finally, we apply the translation theorem to obtain various relationships involving the modified analytic function space Fourier-Feynman transform. Our approach is a new and interesting method to explain some physical phenomenon. 相似文献
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9.
《Integral Transforms and Special Functions》2012,23(10):836-848
The generalized Parseval equality for the Mellin transform is employed to prove the Plancherel-type theorem in L2 with the respective inverse operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform). Moreover, involving the convolution method, which is based on the double Mellin–Barnes integrals, the corresponding convolution and Titchmarsh's theorems for the half-Hartley transform are established. As an application, we consider solvability conditions for a homogeneous integral equation of the second kind involving the Hartley kernel. 相似文献
10.
《Integral Transforms and Special Functions》2012,23(12):955-968
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the convolution method, which is based on the Mellin–Barnes integrals, we prove the corresponding convolution and Titchmarsh's theorems for the half-Hilbert transform. Some applications to the solvability of a new class of singular integral equations are demonstrated. Our technique does not require the use of methods of the Riemann–Hilbert boundary value problems for analytic functions. The same approach is applied recently to invert the half-Hartley transform and to establish its convolution theorem. 相似文献
11.
We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and
first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
We investigate multi-variable integrals of products of sinc functions and show how they may be interpreted as volumes of symmetric convex polyhedra. We then derive an explicit formula for computing such sinc integrals and so equivalently volumes of polyhedra. 相似文献
13.
In this article, we use the translation theorem to obtain several relationships involving integral transforms and convolution products. In particular, we obtain several useful formulas involving various functionals, which arise naturally in quantum mechanics. 相似文献
14.
Some boundaries about the solution of the linear Volterra integral equations of the second type with unit source term and positive monotonically increasing convolution kernel were obtained in Ling, 1978 and 1982. A method enabling the expansion of the boundary of the solution function of an equation in this type was developed in I. Özdemir and Ö. F. Temizer, 2002.
In this paper, by using the method in Özdemir and Temizer, it is shown that the boundary of the solution function of an equation in the same form can also be expanded under different conditions than those that they used.
15.
《Integral Transforms and Special Functions》2012,23(6):491-512
In this paper, we first establish a formula for the conditional generalized Feynman integral of the first variation of a functional F(x) with x in a very general function space C a , b [0, T]. We then use this basic formula to obtain several integration by parts formulas for conditional generalized Feynman integrals and conditional generalized Fourier–Feynman transforms. 相似文献
16.
《Integral Transforms and Special Functions》2012,23(4):259-276
We continue to investigate boundedness properties in a two-parametric family of Lebesgue spaces for convolutions related to the Fourier and Kontorovich–Lebedev transforms. Norm estimations in the weighted L p -spaces are obtained and applications to the corresponding class of convolution integral equations are demonstrated. Necessary and sufficient conditions are found for the solvability of these equations in the weighted L 2-spaces. 相似文献
17.
《Integral Transforms and Special Functions》2012,23(4):345-362
In this paper, we define an L_p analytic Fourier-Feynman transform on C_{0}(B) , the space of abstract Wiener space valued continuous functions on [0, T] . We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C_{0}(B) having the form F(x)= f( (h_1, x(s_1))^{sim}, ldots, (h_m,x(s_n))^{sim}) . Moreover we present various relationships involving convolution and the transforms. 相似文献
18.
《Integral Transforms and Special Functions》2012,23(5):398-411
We consider mapping properties of the iterated Stieltjes transform, establishing its new relations with the iterated Hilbert transform (a singular integral) on the half-axis and proving the corresponding convolution and Titchmarsh's type theorems. Moreover, the obtained convolution method is applied to solve a new class of singular integral equations. 相似文献
19.
Fractional cosine transform (FRCT) and fractional sine transform (FRST), which are closely related to the fractional Fourier transform (FRFT), are useful mathematical and optical tool for signal processing. Many properties for these transforms are well investigated, but the convolution theorems are still to be determined. In this paper, we derive convolution theorems for the fractional cosine transform (FRCT) and fractional sine transform (FRST) based on the four novel convolution operations. And then, a potential application for these two transforms on designing multiplicative filter is presented. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
20.
《Integral Transforms and Special Functions》2012,23(8):573-586
In this paper, we use a Gaussian process to define a generalized integral transform (GIT) and a generalized convolution product (GCP) of functionals defined on a function space. We establish the existence and some properties for the GIT, the GCP and the inverse integral transform. Finally, we prove a Fubini theorem for the GIT and the GCP. 相似文献