Geodesic
Positivity Conditions for Operators with Difference Kernels in Reflexive Spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 3-13

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Using methods of the theory of discrete and integral Fourier transforms, we obtain necessary and sufficient conditions of the positivity of linear discrete, integral, and integro-differential operators with difference kernels in the spaces ${\ell}_p$ and $L_p$ for $1$ and present examples illustrating the results obtained.
Keywords: positive operator, convolution operator, generalized operator of potential type, singular operator, integro-differential operator. 
@article{INTO_2018_149_a0,
     author = {S. N. Askhabov},
     title = {Positivity {Conditions} for {Operators} with {Difference} {Kernels} in {Reflexive} {Spaces}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--13},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a0/}
}
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S. N. Askhabov. Positivity Conditions for Operators with Difference Kernels in Reflexive Spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 3-13. http://geodesic.mathdoc.fr/item/INTO_2018_149_a0/