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On the identity of minimal and maximal realizations related to Fourier series operators. (English) Zbl 0754.42009
The paper studies the Fourier series operator \[ (L(x,D)\varphi)(x):=(2\pi)^{-n}\sum_{l\in \mathbb{Z}^ n} L(x,l)\varphi_ l e^{i(l,x)} \] on a certain subspace \(B^ \pi_{p,k}\) of the periodic distributions defined on \(\mathbb{R}^ n\). Here \(\varphi_ l\) denotes the Fourier coefficient of the distribution \(\varphi\). Under certain conditions on the symbol \(L(x,l)\), the author studies the identity of the maximal and minimal realizations of the operator \(L(x,D)\).
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
47G30 Pseudodifferential operators
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