Approximation of Some Classes of Functions by Fourier_Haar Series

Student: Yankelevich Boris

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2024

In this paper we consider the basic concepts of the Haar system. Solve the problems for the linear function y = qx + b and the quadratic function y = x 2. Let us formulate and prove the formula theorem for the coefficients and partial sum of the Fourier Haar series, the kernel form theorem, the convergence of the sequence of partial sums of the Fourier-Haar series to the continuous function. Consider the class H_w, formulate theorems on the convergence of functions from this class. Consider the Lipschitz class as a special case of the class H_w. Let’s prove the Haar partial sum theorem as the best approximation polynomial in Euclidean norm.

Full text (added June 5, 2024)

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