On generalized difference equations
Bosák, Miroslav ; Gregor, Jiří
Applications of Mathematics, Tome 32 (1987), p. 224-239 / Harvested from Czech Digital Mathematics Library
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In this paper linear difference equations with several independent variables are considered, whose solutions are functions defined on sets of $n$-dimensional vectors with integer coordinates. These equations could be called partial difference equations. Existence and uniqueness theorems for these equations are formulated and proved, and interconnections of such results with the theory of linear multidimensional digital systems are investigated. Numerous examples show essential differences of the results from those of the theory of (one-dimensional) difference equations. The significance and the correct formulation of initial conditions for the solution o partial difference equation is established and methods are described, which make it possible to construct the solution algorithmically. Extensions of the theory to some special nonlinear partial difference equations are also considered.

Publié le : 1987-01-01
Classification:  39A10,  65N20,  65Q05,  93C35 
@article{104253,
     author = {Miroslav Bos\'ak and Ji\v r\'\i\ Gregor},
     title = {On generalized difference equations},
     journal = {Applications of Mathematics},
     volume = {32},
     year = {1987},
     pages = {224-239},
     zbl = {0632.39005},
     mrnumber = {0895880},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104253}
}

Bosák, Miroslav; Gregor, Jiří. On generalized difference equations. Applications of Mathematics, Tome 32 (1987) pp. 224-239. http://gdmltest.u-ga.fr/item/104253/

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