In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.
1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. I...1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. In [2], Coifman and Meyer proved that the operator σ(x, D) is bounded in L~2(R~n) if its symbold (x, ξ) satisfies:展开更多
This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe...This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.展开更多
Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitatire representation of uncertainty principle.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.
基金Project supported by the Science Fund of the Chinese Academy of Sciences.
文摘1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. In [2], Coifman and Meyer proved that the operator σ(x, D) is bounded in L~2(R~n) if its symbold (x, ξ) satisfies:
文摘This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.
文摘Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitatire representation of uncertainty principle.
