The discrete convolution operator Dm[β]
Kholmat Shadimetov)Tashkent State Transport University, Odilkhodjaev str. 1, Tashkent 100167, UzbekistanShermamat Esanov)Termez State University, Barkamol avlod str. 43, Termez 190111, Uzbekistan
ABI
Аннотация
The discrete analogues of certain differential operators of order 2m play important role in construction of optimal formulas of approximate integration, interpolation formulas and difference schemes. In the present paper, in the Sobolev space H2(m)(0,1), the discrete analogue Dm[β] of the differential operator L=∑k=0m(km)(−1)kd2(m−k)dx2(m−k) is constructed, i.e., the discrete equation Dm[β]*εm[β]=δ[β] of the convolution form is solved. Furthermore, it is proved several properties of this discrete operator.
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