vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2024-60-1-15-28vestifm-759Research ArticleМАТЕМАТИКАMATHEMATICSРяды Фурье для многомерно-матричных функций векторной переменнойFourier series for the multidimensional-matrix functions of the vector variableМухаВ. С.MukhaV. S.

Муха Владимир Степанович – доктор технических наук, профессор, профессор кафедры информационных технологий автоматизированных систем

ул. П. Бровки, 6, 220013, Минск

Vladimir S. Mukha – Dr. Sc. (Engineering), Professor, Professor of the Department of Information Technologies of Automated Systems

6, P. Brovka Str., 220013, Minsk

Белорусский государственный университет информатики и радиоэлектроникиBelarusian State University of Informatics and Radioelectronics2024020420246011528Copyright © Муха В.С., 20242024Муха В.С.Mukha V.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/759

В статье развивается теория рядов Фурье по ортогональным многомерно-матричным полиномам. Приводятся известные результаты теории ортогональных полиномов векторной переменной и рядов Фурье и представлены новые результаты. В частности, известные результаты теории рядов Фурье распространяются на случай многомерно-матричных функций, что позволяет решать более общие задачи аппроксимации. Выполнена программная реализация общего случая аппроксимации многомерно-матричной функции векторного аргумента рядом Фурье по ортогональным многомерно-матричным полиномам и подтверждена ее работоспособность. Получены также аналитические выражения коэффициентов полиномов и рядов Фурье второй степени для возможных аналитических исследований.

In the article, the theory of the Fourier series on the orthogonal multidimensional-matrix (mdm) polynomials is developed. The known results from the theory of the orthogonal polynomials of the vector variable and the Fourier series are given and the new results are presented. In particular, the known results of the Fourier series theory are extended to the case of the mdm functions, what allows us to solve more general approximation problems. The general case of the approximation of the mdm function of the vector argument by the Fourier series on the orthogonal mdm polynomials is realized programmatically as the program function and its efficiency is confirmed. The analytical expressions for the coefficients of the second degree orthogonal polynomials and Fourier series for possible analytical studies are obtained.

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The authors declare that there are no conflicts of interest present.