Abstract
1 Introduction The Levy Laplacian was first introduced by P. Levy in studying functionals on L~2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined Levy Laplacian Δ_L via the second variation of a U-functional and proved that Δ_L annihilates functionals of square integrable (cf. Refs. [3, 4]). InRef. [3], Hida and Sait proved the following formula: Δ_L(?)=-(?)- (Δ_LF)~^, where F is Kuo’s Fourier transform of F. In Ref. [4], according to the original idea of P. Levy a definition of the Levy Laplacian was proposed. In the present note we will give a new ex-
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.