Trudy Mat. Inst. Steklov., 1987, Volume 180

JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

1987, Volume 180

Contents

Theory of functions and related questions of analysis

Proceedings of a conference on function theory honoring the 80th birthday of Academician Sergej Mikhajlovich Nikol'skij. Collection of papers

	S. M. Nikol'skij and the Soviet School of approximation theory N. P. Korneichuk		3
	On the works of S. M. Nikol'skij in the theory of differentiable functions of several variables L. D. Kudryavtsev		12
	On extension with preservation of smoothness class and on existence of traces of functions in spaces used in particle transport theory V. I. Agoshkov		23
	On the approximation of the solution of integral equations in potential theory M. Azizov		24
	On the membership of the gradient of a harmonic function in S. M. Nikol'skij's class Sh. A. Alimov		25
	Approximation of functions continuous on a half-line by Szasz–Mirak'yan operators N. T. Amanov		27
	On the approximation of functions by harmonic polynomials V. V. Andrievskii		28
	On a boundary value problem of mathematical physics for a hyperbolic system of equations O. Yu. Anferov, M. A. Galakhov		29
	The approximation of sobolev classes of functions by sums of products of functions of fewer variables M.-B. Babayev		30
	A sharp constant in the Jackson inequality in $L^2$ in the case of a small argument of the modulus of continuity A. G. Babenko		32
	Nonsymetric approximations and inequalities for rearrangements in extremal problems of approximation theory V. F. Babenko		33
	On inequalities for polynomials with real roots V. F. Babenko, S. A. Pichugov		35
	Uniform asymptotic representations of orthogonal polynomials and their derivatives V. M. Badkov		36
	Application of Banach's principle to the solution of a certain type of integral equation S. V. Baev		38
	On inequalities for trigonometric polynomials M. P. Barykin, Ya. S. Bugrov, A. P. Uninskij		39
	On approximation of the classes $C(\varepsilon)$ by linear polynomial operators V. A. Baskakov		41
	On constuction of approximate solutions of boundary value problems for certain classes of ordinary differential equations I. I. Bezvershenko		43
	Linear methods for summing Fourier–Laguerre series B. Bekzatov		44
	Approximation by a “floating” system of exponentials on classes of periodic smooth functions È. S. Belinskii		46
	On a constructive characterization of classes of functions admitting quasiconformal extension V. I. Belyi, V. V. Maimeskul		47
	Convexity of Banach spaces and imbedding theorems M. Z. Berkolaiko		49
	Imbeddings of an anisotropic Sobolev space for a domain with the flexible Horn condition O. V. Besov		50
	Convergence tests for branching continued fractions D. Ī. Bodnar		52
	On the absolute summability of Fourier integrals by the G. F. Voronoj method L. G. Boitsun		53
	On absolute summability of Fourier integrals with multipliers L. G. Boitsun, A. I. Khalyuzova, A. I.		54
	On boundary properties of holomorphic functions A. V. Bondar'		56
	A remark on the parabolic theorem on convergence of continued fraction V. A. Borodin		57
	The conjugate Franklin system is a basis in the space of continuous functions S. V. Bochkarev		58
	Extension of functions with preservation of smoothness Yu. A. Brudnyi, P. A. Shvartsman		60
	On an estimate of approximation of continuous functions of two variables on a finite square by certain algebraic polynomials V. P. Bugaets		62
	Linear methods of summing Fourier series and fractional difference operators Ya. S. Bugrov		63
	Multiple powers and local approximations A. P. Bulanov		65
	Approximation by infinitely differentiable functions with preservation of boundary values V. I. Burenkov		68
	Asymptotic estimates of the partial sums of certain Dirichlet series V. P. Burlachenko		70
	A best quadrature formula with weight for a certain class of functions T. N. Busarova		71
	Traces of functions in Sobolev spaces with metric generated by a symmetric norm A. V. Bukhvalov		72
	Best approximation in the mean of multiply monotone functions A. V. Bushanskii		74
	Investigation of questions of approximation of convex surfaces by bilinear splines V. F. Byzov, V. A. Zavsegdashnii		75
	On solution of weakly singular integral equations by the method of mechanical quadratures G. M. Vainikko, A. Pedas		76
	On approximation of functions of two variables by generalized polynomials S. B. Vakarchuk		77
	On a geometric method of reconstructing space curves arcs of geodesic circles on cylindrical surfaces B. S. Vakarchuk, P. T. Stepanenko		79
	Optimal reconstruction of functions of several variables A. V. Vasilenko		80
	Approximation in a Banach space by a convergent sequence of subspaces of fixed dimension V. L. Velikin		81
	A development of the method of quadratures for the Laplace equation and conformal mappings E. A. Volkov		83
	On approximation in the mean by multidimensional positive linear operators Yu. I. Volkov		85
	On a characterization of functions in the class $C_0^\psi L_\infty$ V. T. Gavrilyuk		86
	On generalized Nikol'skii–Besov spaces on the sphere A. D. Gadzhiev, Kh. P. Rustamov		87
	On degrees of smoothness, moduli of continuity and classification of continuous functions V. D. Galan, D. M. Galan		89
	A direct and inverse theorem on approximation by polynomials on the $m$- dimensional ball M. I. Ganzburg		91
	On the approximation of functions of several variables by linear means L. D. Gogoladze		92
	On the imbedding of a Nikol'skij–Besov space in a weighted Lorentz space M. L. Gol'dman		93
	Nonlinear capacity and extension of differentiable functions V. M. Gol'dstein		95
	An inverse theorem on approximation of functions by operators of extension to a canonical domain V. I. Gorbaichuk		97
	Approximation of periodic functions by linear operators A. N. Davidchik, A. A. Ligun		98
	Approximate solution of nonlinear integral equations with the help of local spline approximation V. P. Danilovich		99
	On best approximation of functions in the spaces $B$ and $H$ A. S. Dzhafarov		100
	On a certain $F$-space of analytic functions I. A. Dzhvarsheishvili		103
	Mapping sets of locally finite length by a rational function E. P. Dolzhenko, V. I. Danchenko		105
	On the choice of knots in approximation by splines in spaces with a weight V. G. Doronin		107
	On the theory of the Cauchy problem in the complex domain Yu. A. Dubinskii		108
	Normal solvability of linear differential operators of infinite order O. V. Epifanov, Yu. F. Korobeinik		110
	On the application of multiplicative systems in numerical information processing A. V. Efimov		112
	Approximation of differentiable periodic functions of two variables by Fourier sums P. V. Zaderej		114
	Optimal precision quadrature formulas for computing integrals of rapidly oscillating functions V. K. Zadiraka		115
	Approximation of certain elementary functions in the metric of $L$ Z. V. Zaritskaya, A. I. Shvaĭ, P. Ē. Antonyuk		117
	On inequalities of Nikol'skij type I. I. Ibragimov, J. I. Mamedkhanov		118
	Optimal precison approximation of functions with singular points unknow in advance V. V. Ivanov		120
	Representation of functions by Bochner–Riesz spherical means in the spaces $\varphi(L)$ V. I. Ivanov		121
	On imbedding theorems for spaces of differentiable functions in domains V. P. Il'in		122
	On equivalent norms in weighted spaces N. I. Imranov		124
	On hypoellipticity weight for a class of regular operators G. G. Kazaryan		125
	On mean convergence of Fourier–Jacobi series with quasimonotone coefficients S. G. Kal'nei		128
	Integral representations and estimates for generalized differences of entire functions of exponential type G. A. Kalyabin		129
	On trigonometric polynomials with coefficients $+1$, $-1$, $0$ B. S. Kashin		131
	A criterion for the existence of the $p$-limit Yu. D. Kashchenko		132
	On the theory of Riesz potentials on Lorentz spaces I. A. Kipriyanov, L. A. Ivanov		134
	Differential properties of an operator of best approximation of complex-valued functions V. V. Kovtunets		135
	Anisotropic maximal functions and potentials in weighted Lorentz spaces V. M. Kokilashvili		136
	Superconvex functions and multiextremal problems A. I. Kosolap		139
	Fourier coefficients and densities of subsets of the series of natural numbers B. D. Kotlyar		140
	On differentiability properties of functions in $H^p$ on the boundary of the disk of convergence V. G. Krotov		141
	On imbedding of space of Nikol'skij–Besov type for different dimensions N. L. Kudryavtsev		142
	Integrability and strong summability of multiple trigonometric series O. I. Kuznetsova		143
	Averaging operators and partial differential equations L. P. Kuptsov		145
	Integral inequalities and boundary properties of monotone functions B. P. Kufarev		146
	On convergence of two-dimensional continued fractions Kh. Kuchmins'ka		147
	Sharp estimates of the widths of convolution classes in the space $C_{2\pi}$ A. K. Kushpel'		148
	On estimates of strong approximation of functions by Fourier–Čebyšev sums V. V. Lipovik		149
	Sharp estimates of the Lebesgue constants of partial sums of multiple Fourier series I. R. Liflyand		151
	Extremal numerical integration formulas for classes of differentiable periodic functions N. E. Lushpai, I. L. Zaichenko		152
	On the approximations of Sobolev classes of functions on $\boldsymbol R^n$ G. G. Magaril-Il'yaev		154
	On inequalities of Bernstein–Nikol'ski type V. E. Maiorov		155
	A constructive description of certain spaces G. A. Mamedov		156
	On the question of improving a theorem of Vallee–Poussin with the help of the Pontryagin maximum principle V. E. Mirakov		158
	Formulas for representing the solution manifold of some systems of complex partial differential equations L. G. Mikhailov		159
	On formulas for the approximate computation of integrals V. P. Motornyi, E. E. Dunaichuk		161
	On a class of functions with variable smoothness L. V. Nasonova		163
	On imbedding theorems for weighted classes of differentiable functions Yu. S. Nikol'skii		165
	Sufficient conditions for integrability of double trigonometric cosine series Yu. L. Nosenko		166
	The Calderon theorem for the pair of spaces $L_1+L_\infty$ and $L_1\cap L_\infty$ V. I. Ovchinnikov		168
	On a way of using the theory of approximation of functions for solving integral equations of the first kind O. P. Okolelov		169
	On efficent approximation of solutions of multipoint boundary value problems L. A. Ostrovetskii		171
	On strong summability of Fourier series in systems of functions of polynomial type N. L. Pachulia		172
	On singular integral convolution operators of weak type B. I. Peleshenko		174
	Approximation numbers and the eigenvalue problem for integral operators S. V. Pereverzev		175
	Asymptotic formulas for the spectrum of a class of Sturm–Liouville boundary value problems O. A. Plaksina		177
	Theorems of Szasz type on absolute convergence of multiple Fourier series of functions in a generalized Lebesgue space B. S. Pozdeev		178
	Absolute and strong $p$th-power summability of double fourier series by matrix methods N. T. Polovina		179
	On an iterative spline-quadrature method for solving integral equations of the second kind R. V. Polyakov		181
	On the approximation of functions by algebraic polynomials M. K. Potapov		182
	Vectors of exponential type and their applications Ya. V. Radyno		184
	On the best mean-square approximation, by polynomials and entire functions of exponential type, to functions with a logarithmic singular point R. A. Raitsin		185
	Atomic functions and approximation theory V. A. Rvachev		186
	Approximation of continuous periodic functions by linear means of their Fourier series V. I. Rukasov		187
	On the imbedding of certain classes of functions on the sphere Kh. P. Rustamov		188
	A problem with an integral condition for an elliptic equation with strong degeneration on the whole boundary J. V. Rybalov		190
	Absolute $(B,p(y)(C,1))$-summability of a Fourier integral T. I. Rybnikova		192
	Direct and inverse imbedding theorems for seminormed spaces O. A. Salieva		193
	On some inequalities for functions in eighted classes and boundary value problems with degeneracy Yu. D. Salmanov		195
	Weighted Zygmund estimates for fractional differentiation and integration, and their applications S. G. Samko, Kh. M. Murdaev		197
	Approximation theorems for a class of functions V. N. Sedov		199
	Theorems of Tauberian type for matrix transformations of series K. M. Slepenchuk		200
	On a criterion for an element of best $(\alpha,\beta)$-approximation in the space of summable functions G. S. Smirnov		201
	Approximation of periodic functions by Fourier sums A. I. Stepanets		202
	On the question of Pade approximation of some special functions V. K. Stolyarchuk		204
	On local approximation by Abel–Poisson sums in Hardy spaces È. A. Storozhenko		206
	Sharp norm estimates on some function classes V. F. Storchai		207
	The error in multidimensional piecewise polynomial approximation Yu. N. Subbotin		208
	On uniqueness of multiple trigonometric series A. A. Talalyan		210
	On an inequality for an intermediate derivative in weighted spaces B. V. Tandit		211
	On estimates of the best bilinear approximations of periodic functions and singular numbers of integral operators V. N. Temlyakov		213
	Uniform approximation by algebraic polynomials of functions on the sphere of an odd-dimensional space A. P. Terekhin		215
	On the distribution of the values of some sequences of algebraic polynomials A. Timan		216
	Constructive characteristics of the properties of Kernels of integral operators and the behavior of their $s$-numbers M. F. Timan, T. N. Semirenko		217
	On the comparison principle for Fourier expansions and existence subspaces in the integral metric R. M. Trigub		219
	On an extension theorem for spaces of functions whose partial derviatives are summable to different powers ($\Omega\in R^n$) B. L. Fain		221
	On the approximation of functions of the Zygmund class by conjugate Cesaro sums L. P. Falaleev		222
	On a variational method in spaces with dominant mixed derivative V. M. Filippov		224
	Application of the $A$-method to the investigation of Pade approximants of elementary functions L. I. Filozof		225
	On the approximation of nonperiodic functions by algebraic polynomials in a eighted integral metric L. B. Khodak		227
	Weighted moduli of variation and their applications Z. A. Chanturiya		228
	Difference operators with variable step V. V. Shan'kov		229
	Addendum to direct approximation theorems of S. M. Nikol'skij type on an interval, and inverse theorems I. A. Shevchuk		230
	On the transcendence and algebraic independence of the values of some classes of analytic functions A. B. Shidlovskii		232
	Estimation of the norm of the error functional for interpolation formulas in the Sobolev space $L_2^{(m)}$ Ts. B. Shoĭnzhurov		234
	On the Fourier sums in $L_p$ V. A. Yudin		235
	Аппроксимационный метод для эллиптических и параболических уравнений P. Janchuk		237
	On the approximation of even and odd bounded $2\pi$-periodic functions by trigonometric polynomials of best uniform approximation at a given system of points N. Ya. Yatsenko		238