Geodesic
Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2019), pp. 94-99

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The paper is devoted to approximate calculation of integrals of products of two functions by the method of tensor products of functionals. Under the assumption that one of them is from the Sobolev class with the dominant mixed derivative, and the other with fast oscillation, there are obtained unimprovable (in the sense of order) estimates of arising errors of approximation. Also, a comparative analysis with known methods in the "theory of oscillations" be conducted.
Keywords: tensor product of functionals, Haar function, highly oscillatory integral, asymptotic method, Filon method, Levin collocation method. 
@article{IVM_2019_11_a11,
     author = {N. Temirgaliyev and S. S. Kudaibergenov and N. Zh. Nauryzbaev},
     title = {Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {94--99},
     publisher = {mathdoc},
     number = {11},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_11_a11/}
}
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N. Temirgaliyev; S. S. Kudaibergenov; N. Zh. Nauryzbaev. Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2019), pp. 94-99. http://geodesic.mathdoc.fr/item/IVM_2019_11_a11/