Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1229.60096
Chung, Hyun Soo; Tuan, Vu Kim
Generalized integral transforms and convolution products on function space. (English)
[J] Integral Transforms Spec. Funct. 22, No. 8, 573-586 (2011). ISSN 1065-2469; ISSN 1476-8291/e

Existence and properties of the generalized integral transform (GIT) and the generalized convolution product function (GCP) on Wiener space are studied. Let $C_0[0,T]=\{x\in C([0,T];\mathbb R):\ x_0=0\}$ and $K_0[0,T]=\{y\in C([0,T];\mathbb C):\ y_0=0\} .$ Let $\mu$ be the Wiener measure on $C_0[0,T].$ For $h\in L^2[0,T], t\in [0,T]$, let $Z_h(x,t)$ be the Paley-Wiener-Zygmund integral of $h$ w.r.t. $x$ over $[0,t],$ which is $\mu$-a.s. defined. For any $\alpha,\beta\in\mathbb C$, and a measurable function $F$ on $K_0[0,T]$, the function $$\mathcal F_{\alpha,\beta,h}(F)(y):= \int_{C_0[0,T]}F(\alpha Z_h(x,\cdot),\beta y)\mu(x),\ \ y\in K_0[0,T]$$ is called the generalized integral transform (GIT) of $F$ if it exists. Moreover, the generalized convolution function of $F$ and $G$ is defined by $$(F\* G)_\alpha(y)= \int_{C_0[0,T]}F\Big(\frac{y+\alpha Z_h(x,\cdot)}{2^{1/2}}\Big)G\Big(\frac{y-\alpha Z_h(x,\cdot)}{2^{1/2}}\Big)\mu(x) ,\ \ y\in K_0[0,T].$$
[Feng-Yu Wang (Swansea)]

MSC 2000:: *60J65 Brownian motion
28C20 Set functions and measures and integrals in infinite-dim. spaces

Keywords: generalized integral transform; generalized convolution product; inverse integral transform Wiener space

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]