PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 79(93), pp. 73–93 (2006) 

THE METHOD OF STATIONARY PHASE FOR ONCE INTEGRATED GROUPRamiz Vugdalic and Fikret VajzovicPrirodnomatematicki fakultet, 75000 Tuzla, Bosnia and Herzegovina and Prirodnomatematicki fakultet, 71000 Sarajevo, Bosnia and HerzegovinaAbstract: We obtain a formula of decomposition for $$ \Phi(A)=A\int\limits_{R^n}{S(f(x))\varphi(x) dx+\int\limits_{R^n}{\varphi(x) dx}} $$ using the method of stationary phase. Here $(S(t))_{t\in R}$ is once integrated, exponentially bounded group of operators in a Banach space $X$, with generator $A$, which satisfies the condition: For every $x\in X$ there exists $\delta=\delta(x)>0$ such that $\frac{S(t)x}{t^{1/2+\delta}}\to 0$ as $t\to 0$. The function $\varphi (x)$ is infinitely differentiable, defined on $R^n$, with values in $X$, with a compact support supp $\varphi$, the function $f(x)$ is infinitely differentiable, defined on $R^n$, with values in $R$, and $f(x)$ on $\operatorname{supp}\varphi$ has exactly one nondegenerate stationary point $x_0$. Keywords: Strongly continuous group; once integrated semigroup (group); method of stationary phase Classification (MSC2000): 47D03; 47D62 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 27 Oct 2006.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
