2019
Том 71
№ 8

# Kushpel A. K.

Articles: 10
Article (Russian)

### On the Lebesgue constants

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1073-1081

UDC 517.5
We give the solution of a classical problem of approximation theory on sharp asymptotic of the Lebesgue constants or norms of the Fourier – Laplace projections on the real spheres $\mathbb{S}^{d},$ complex $\mathrm{P}^{d}(\mathbb{C})$ and quaternionic $\mathrm{P}^{d}(\mathbb{H})$ projective spaces, and the Cayley elliptic plane $\mathrm{P}^{16}(\mathrm{Cay}).$ In particular, these results extend sharp asymptotic found by Fejer in the case of $\mathbb{S}^{1}$ in 1910 and by Gronwall in 1914 in the case of $\mathbb{S}^{2}$ .

Article (Ukrainian)

### Estimation of the widths of classes of smooth functions in the space

Ukr. Mat. Zh. - 1990. - 42, № 2. - pp. 279–280

Article (Ukrainian)

### Estimates of the diameters of convolution classes in the spaces C and L

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1070–1076

Article (Ukrainian)

### An estimate of the rate of convergence of the derivative of the interpolation polynomial on classes of differentiable functions

Ukr. Mat. Zh. - 1988. - 40, № 2. - pp. 231-234

Article (Ukrainian)

### A family of extremal subspaces

Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 786-788

Article (Ukrainian)

### Convergence rate of fourier series and best approximations in the space Lp

Ukr. Mat. Zh. - 1987. - 39, № 4. - pp. 483–492

Article (Ukrainian)

### Behavior of Lebesgue constants for linear methods of summing fourier series giving the best order approximation

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 185-190

Article (Ukrainian)

### Interpolation of periodic functions

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 114–116

Article (Ukrainian)

### A method for the approximation of periodic functions

Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 774 – 776

Article (Ukrainian)

### A method of reconstruction of differentiate periodic functions by trigonometric polynomials

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 507 – 512