Geodesic
Pseudodifference operators and their Green's functions
Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 605-622.

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The author studies pseudodifference operators on a discrete metric space, where the matrix elements of the operators decrease faster than a system of singular functions of the distance between points determining a matrix element. Similar estimates for matrix elements are proved for the inverse of a pseudodifference operator in the case where the weight functions increase faster than any function of the volume (the number of points in the ball of radius $r$ with prescribed center) and slower than the standard exponential function. Bibliography: 12 titles. 
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M. A. Shubin. Pseudodifference operators and their Green's functions. Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 605-622. http://geodesic.mathdoc.fr/item/IM2_1986_26_3_a6/

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