Geodesic
On the Solvability of the Cauchy Problem for a Polynomial Difference Operator
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 3, pp. 83-94

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In this paper we consider a variant of the Cauchy problem for a polynomial difference operator. A formula representing the solution to the problem via its fundamental solution is obtained, the conditions for its solvability are given. In particular, in two-dimensional case a rather simple condition in terms of coefficients of the operator symbol is proved. Besides that, a recurrence relation for principal minors of the matrix corresponding to the difference operator is obtained.
Keywords: difference operator, fundamental solution. 
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     author = {M. S. Rogozina},
     title = {On the {Solvability} of the {Cauchy} {Problem} for a {Polynomial} {Difference} {Operator}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a6/}
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M. S. Rogozina. On the Solvability of the Cauchy Problem for a Polynomial Difference Operator. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 3, pp. 83-94. http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a6/