1 Introduction The Lévy Laplacian was first introduced by P. Lévy in studying functionals on L^2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined L...1 Introduction The Lévy Laplacian was first introduced by P. Lévy in studying functionals on L^2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined Lévy 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. Lévy a definition of the Lévy Laplacian was proposed. In the present note we will give a new ex-展开更多
基金Supported by the National Natural Science Foundation of China ( 11061032,30973586)the Young Fund of Northwest University for Nationalities (X2009-003)
基金Research supported by the National Natural Science Foundation of China
文摘1 Introduction The Lévy Laplacian was first introduced by P. Lévy in studying functionals on L^2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined Lévy 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. Lévy a definition of the Lévy Laplacian was proposed. In the present note we will give a new ex-
基金Supported by NSFC(No.11061032)Colleges and Universities Scientific Research Plan of Gansu Province for Postgraduate Tutor(No.1205-07)Colleges and Universities Fundamental Research Funds Project of Gansu Province(2012)
基金Supported by National Natural Science Foundation of China(71561017)Science and Technology plan of Gansu Province(145RJZA033)Special Funds for Scientific Research of Lanzhou Finance and Economics University
