Abstract
Two generalizations of Spitzer–Stone theorem are given. This theorem (1960) shows a deep link between the asymptotic behaviour of the elements of (T N ( f)) −1, where T N ( f) is the Toeplitz matrix associated to the singular symbol f of order 2, and the Green kernel of the second derivative operator. An exact expression of the inverse is obtained for a particular family, the second result is concerned by an asymptotic expansion for a general family.
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