### TOMIC FUNCTIONS AND LACUNARY INTERPOLATION SERIES IN BOUNDARY VALUE PROBLEMS FOR PARTIAL DERIVATIVES EQUATIONS AND IMAGE PROCESSING

#### Abstract

_{j}(x) –analogues of the basic functions of the generalized atomic Taylor expansions are obtained – which are needed for lacunary (Birkhoff) interpolation. For the applications in variational and collocation methods for solving bondary value problems for partial derivative and integral equations the tomic functions ftup

_{r,j}(x) are obtained that are analogues of B-splines and atomic functions fup

_{n}(x). Using similar methods, the tomic functions based on other atomic functions such as Ξ

_{n}(x) can be obtained.

#### Keywords

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DOI: https://doi.org/10.32620/reks.2020.1.06

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