In this note we prove that every classical 1-periodic pseudodifferential operator A of order can be represented in the form
where and are -smooth 1-periodic functions and are 1-periodic functions or distributions with Fourier coefficients and sign with respect to the trigonometric orthonormal basis of . Some explicit formulae for are given. The case of operators of order is discussed, too.
Cite this article
Gennadi Vainikko, An Integral Operator Representation of Classical Periodic Pseudodifferential Operators. Z. Anal. Anwend. 18 (1999), no. 3, pp. 687–699DOI 10.4171/ZAA/906