Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theor...Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.展开更多
Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-va...Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-valued generalized functional space. A characterized theorem is obtained by using their S-transform.展开更多
The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination o...Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties （Poincare invariance and irreducibility） of the solutions are discussed.展开更多
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
文摘Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.
文摘Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-valued generalized functional space. A characterized theorem is obtained by using their S-transform.
文摘The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
基金supported by NSFC (10401011,10871153)China Postdoctoral Science Foundation (2005037660)
文摘Under the framework of white noise analysis, the existence of scattering solutions to the abstract dynamical φ4^4 wave equations in terms of generalized operators （see Section 3 below） is proven via a combination of the characterization for the symbol of generalized operators and the classical scattering results. In addition, some properties （Poincare invariance and irreducibility） of the solutions are discussed.
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-
