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Soviet Mathematics DOKLADY Volume 43 1991 A Translation of the Mathematics Section of JIOKJIA JIbI AKAJEMUU HAYK CCCP TOM 316-318 1991 a American Mathematical Society | 8 Providence, Rhode Island USA ISSN 0197-6788 SOVIET MATHEMATICS—DOKLADY Translation edited by Ben Silver with the assistance of Ralph Sizer A translation of the mathematics section of AOKJIAbI AKAJIEMMM HAYK CCCP VUsnatensctso “Hayxa”, 1991 r. Each issue corresponds to one volume of the Soviet Doklady, which is issued three times a month, six issues constituting a volume. SUBSCRIPTION INFORMATION. Soviet Mathematics—Doklady is published six times per year. Subscription prices for Volumes 42-43 (1991) are $602 list, $482 institutional member, $361 individual member. A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. 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Translation authorized by the All-Union Agency for Author’s Rights, Moscow. The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. 6) This publication was typeset using A,4S-TEX, the American Mathematical Society’s TEX macro system. 10987654321 9796949 953 9 2 SOVIET MATHEMATICS — DOKLADY Volume 43, Number 1 July-August 1991 CONTENTS Asratyan, A. S. and Mirumyan, A. N. Transformations of edge colorings of a bipartite multigraph, and their applications Boimatov, K. Kh. Multidimensional spectral asymptotics for elliptic operators in domains satisfying the cone condition Brykalov, S. A. Existence and nonuniqueness of solutions of some nonlinear boundary value problems Vavilov, S. A. On the solvability of a class of operator equations Davtyan, A. A. On the spaces wm and coercive properties of equations of elliptic Elkin, V. I. Automorphisms and decomposition of affine control systems Ershov, Yu. L. Characterization of Kochen rings of PCy-fields Zvyagin, M. Yu. Second order equations reducible to zx, = 0 by a Backlund transformation Sabitov, K. B. On the spectrum of a gas dynamics problem of Frankl’ for equations of mixed type Temlyakov, V. N. On universal cubature formulas Shamaey, I. I. Operators of diffusion type Gomilko, A. M. and Radzievskii, G. V. Equiconvergence of series in eigenfunc- tions of ordinary functional-differential operators Gorbunov, K. Yu. Context-free decidability of graphs that do not realize a plane lattice Guliev, V. S. On the boundedness of singular integral operators on the Heisenberg group in weighted generalized Holder spaces and weighted L,-spaces Gurvich, V. A. and Khanin, K. M. A Gaussian distribution for sums of distances Denisov, V. N. Stabilization of solutions of parabolic equations, and the central limit theorem Kravchenko, V. G. and Shaev, A. K. The theory of solvability of singular integral equations with a linear-fractional Carleman shift Maksudov, F. G., Allakhverdiev, B. P., and Bairamov, E. M. On the spectral theory of a nonselfadjoint operator generated by an infinite Jacobi matrix Pogorelov, A. V. On a theorem of Beltrami Roitberg, Ya. A. The Cauchy problem for general hyperbolic systems in a complete scale of spaces of Sobolev type Starkov, A. V. On majorant optimization of weighted algorithms in the Monte Carlo method Strugov, Yu. F. On homeomorphism of Q,-extremal mappings Yulmukhametov, R. S. Homogeneous convolution equations Yunusov, M. Yu. A two-sided power boundary layer in nonlocal problems Agadzhanov, A. N. Strictly nuclear imbeddings and interpolation of Sobolev spaces of infinite order Akhiev, S. S. and Sanieva, S. N. On problems of Cauchy and Goursat type on composite lines Bronshtein, M. D. and Cherevatskii, A. S. Variational problems for functionals determined by the maximum of a Lagrangian Gurvich, V. A. and Khanin, K. M. A Poisson distribution for the number of pairs of close points Eremenko, A. E. and Sodin, M. L. On the distribution of values of meromorphic functions of finite order Kazaryan, K. S. and Ul’yanov, P. L. On a problem of Alexits with respect to divergence of orthogonal Fourier series Kolesov, A. Yu. A new class of relaxation systems in general position Petrushko, I. M. On the boundary values of solutions of second-order parabolic equations degenerate on the boundary of the domain Rakhmetov, N. K. On the uniqueness of an element of best approximation in certain function spaces Abasov, M. T., Rasulov, M. A., Ibragimov, T. M., and Ragimova, T. A. On a method of solving the Cauchy problem for a first-order nonlinear equation of hyperbolic type with a smooth initial condition Avdonin, S. A., Ivanov, S. A., and Ishmukhametov, A. Z. A quadratic problem of optimal control of the vibrations of a string Aliev, I. A. and Gadzhiev, A. D. Weighted estimates of singular integrals generated by a generalized shift operator Aseev, V. V. On extremal mappings of dihedral wedges Akhtamova, S. S. and Belov, Yu. Ya. On some inverse problems for parabolic equations Babin, A. V. The asymptotic behavior as |x| — oo of strongly perturbed Poiseuille Belov, Yu. Ya. and Savateev, E. G. On an inverse problem for a parabolic equation with an unknown coefficient on the time derivative Danilov, L. I. Estimates of the Poisson kernel for a tube domain over a pointed Kamynin, V. L. Asymptotic behavior of solutions of the Cauchy problem for nondivergence parabolic equations Levitskii, B. E. The reduced p-modulus and the inner p-harmonic radius Melikyan, A. A. Optimal guaranteeing control of a dynamical system with search for a goal point Rodionov, E. D. Compact periodic standard Einstein manifolds Samoilenko, A. M. and Ilolov, M. On the theory of evolution equations with impulsive action Sobolevskii, E. P. and Sobolevskii, P. E. The commutant method and coercive- ness of the Cauchy problem Khisamutdinov, A. I. Algorithms with “different time coordinates” in Monte Carlo methods for the nonlinear “smoothed” Boltzmann equation Amirov, R. Kh. Integral geometry and the problem of determining a Riemannian metric Belov, Yu. Ya. On an inverse problem for a semilinear parabolic equation Zarkh, M. A. A value function criterion in a linear differential game Ivanov, A. A. A geometric approach to the question of uniqueness for sporadic simple groups Katrakhov, V. V. Singular boundary value problems for some elliptic equations in domains with corner points Salakhitdinov, M. S. and Islomov, B. Boundary value problems for an equation of mixed type with two interior lines of degeneracy Sushchanskii, V. I. Wreath products and general products of groups Tret’ yak, A. I. On necessary conditions for optimality of even order in the time- optimal problem for a class of control systems Trubin, V. A. On the determination of the strength of a graph Belyankov, A. Ya. Formal apparatus of the method of exhaustion in linear alge- Didenko, V. D. Para-algebras and approximate solution of singular integrodif- ferential equations Zubov, V. I. Interpolation and approximation of probability distributions Lyskova, A. S. Orthogonal polynomials in several variables Moiseev, E. I. On a problem of Lions Radkevich, E. V. The Gibbs-Thompson correction and conditions for the existence of a classical solution of the modified Stefan problem Sarymsakov, T. A. and Ganikhodzhaev, N. N. On the ergodic principle for quadratic processes Sedenko, V. I. Uniqueness of the generalized solution of an initial-boundary value problem in the nonlinear theory of vibrations of shallow shells Strunkov, S. P. Generalizations of Euler’s divisibility theorem and other arithmetic properties of representations of finite permutation groups Sychev, M. A. On the regularity of solutions of some variational problems Chistyakov, G. P. On the convergence of n-fold convolutions of distribution laws with infinitely divisible distribution laws Table of Contents for the next issue (Vol. 43, No. 2, September-October 1991, Russian original Tom 317, nos. 1-6) Volume 43, Number 2 September-October 1992 CONTENTS Vakhrameev, S. A. A theorem on the Morse index of the extremals of some optimal control problems Gabasov, R. and Kirillova, F. M. Dual optimization for dynamical systems ... Dzhuraev, T. D. and Abdinazarov, S. A nonclassical boundary value problem for a higher order equation with multiple characteristics Ivanov, V. K. and Mel’nikova, I. V. New generalized functions and weak well- posedness of operator problems Il’in, V. A. On equiconvergence with a trigonometric series of expansions in root functions of the Schrédinger operator with an arbitrary summable complex- valued potential Imanaliev, M. I. and Asanov, A. On solutions of systems of nonlinear two- dimensional Volterra integral equations of the first kind Mitropol’skii, Yu. A. and Kurbanov, I. On the solvability of boundary value problems of electromagneto-elasticity with memory Muravei, L. A. and Filinovskii, A. V. On a parabolic boundary value problem . Nikol’skii, S. M. Approximation of functions by polynomials on a manifold ... Barskii, I. L. On the behavior of the spectrum of certain linear multipoint boundary value problems for ordinary differential equations Bobylev, N. A. and Burman, Yu. M. Morse lemmas for integral functionals ... Boimatov, K. Kh. Multidimensional distribution functions for degenerate elliptic operators Vinogradov, M. M. On a general algebraic theory of linear differential operators. Galaktionov, V. A. On the peaking set for a nonlinear diffusion and combustion equation Imanaliev, M. I. and Sharipov, S. The burst phenomenon in the theory of integral equations of Volterra type of the first kind Kosmodem’ yanskii, A. A., Jr. A theorem on representation of the solution of the second boundary value problem Kochergin, V. V. On the complexity of computations in finite abelian groups .. Kucherov, A. B. A fast iterative method for solving in real arithmetic a system of linear equations with a complex symmetric matrix Labudovich [Labudovi¢], N. and Pavichevich, Zh. [Z. Pavitevi¢] Hyperbolic Bloch functions Liskovets, O. A. Regularization of ill-posed mixed variational inequalities Mel'nik, V. S. On some properties of solutions of operator equations and variational inequalities Pavichevich, Zh. [Zarko Pavitevi¢é] Carleson measure, the Ahlfors-Shimizu char- acteristic, and the classes BMO and BMOA Pokotilo, V. G. Optimization of a priori observations Sandrakov, G. V. On a problem of H. Poincaré Almamedov, M. S., Bairamogly, M., and Katanova, V. I. Trace formulas for a differential equation of even order with unbounded operator coefficient ... Balaev, M. K. On well-posed solvability of differential-operator equations of arbitrary order Boimatov, K. Kh. Spectral asymptotics of nonselfadjoint pseudodifferential operators in bounded domains Gavrilenko, Yu. V. Correct classes of computations in logic programming Gadzhiev, A. G. Control of queueing systems in a class of delays Zhidkov, P. E. On an invariant measure for a nonlinear Schrodinger equation . Zhuravlev, I. V. Recovery of a mapping from the normalized Jacobi matrix . Zakharevich, I. S. Spectral problems for the Sturm-Liouville equation with a parameter. Geometry of finite-gap potentials Krygin, A. V., Sukochev, F. A., and Chilin, V. I. Uniform convexity and local uniform convexity of symmetric spaces of measurable operators Kudryavtsev, L. D. On estimating a function on an infinite interval Lerner, M. E. On the formulation and solvability of a class of boundary value problems for the Lavrent' ev-Bitsadze equation Pestov, V. G. Nonstandard hulls of normed Grassmann algebras and their applications in superanalysis Pletner, Yu. D. On some properties of solutions of the equation for gravitational- gyroscopic waves Pospelov, A. S. Some estimates of the Gibbs function for partial sums of Fourier series in A-multiplicative systems Sandrakov, G. V. Evolution of resonances under perturbation of a system with constant frequencies Serov, V. S. On recovering the potential in a three-dimensional problem of scat- tering theory Tersenov, S. A. On the first boundary value problem for a direct-inverse parabolic equation Tolstonogov, A. A. Extremal selections of multivalued mappings and the “bang- bang” principle for evolution inclusions Almamedov, M. S. and Katanova, V. I. On regularization of the trace of a higher- order differential operator with a bounded operator coefficient Berezhnoi, E. I. Weighted inequalities of Hardy type in general ideal spaces ... Berest, Yu. Yu. Construction of fundamental solutions for Huygens’ equations as invariant solutions Borsuk, M. V. Best-possible estimates of solutions of the Dirichlet problem for linear elliptic nondivergence equations of second order in a domain with a conical point Varlamov, V. V. Asymptotic behavior of the energy for an integro-differential equation describing acoustic waves in a relaxation medium Vu Kim Tuan and Nguen Tkhan’ Khai [Nguyen Thanh Hai] On a class of multidimensional Watson integral transforms Golovin, V. D. Homologically trivial spaces Gulisashvili, A. B. The mean e-dimension of function classes with spectra con- tained in a given set Derkach, V. A. On generalized resolvents of a class of Hermitian operators in a Krein space Dzhangibekov, G. A linear junction problem for solutions of elliptic systems of differential equations with singular coefficients in the plane Dzhuraev, A. On a boundary value problem for the Moisil-Teodorescu system of equations Kachurovskii, A. G. A fluctuation ergodic theorem Kuz’ minykh, A. V. A continuous function whose graph intersects the graph of each polynomial in a set of cardinality of the continuum Mynbaev, K. T. Approximate solution of a Fredholm integral equation of the second kind in a multidimensional domain 543 Nazaikinskii, V. E., Sternin, B. Yu., and Shatalov, V. E. On an application of the Maslov operator method to a diffraction problem 547 Popa, M. N. Application of invariant processes to the study of homogeneous linear partial integrals of a differential system 550 Shirinbekov, M. On Hartogs’ theorem in classes of nonanalytic functions 556 Shishkin, G. I. A difference approximation of a singularly perturbed quasilinear elliptic equation degenerating into a first-order equation 562 Beklaryan, L. A. On a method of regularization of boundary value problems for differential equations with deviating argument 567 Bronshtein, M. D. and Cherevatskii, A. S. A variational method of solving boundary value problems for ordinary differential equations 572 Dzhuraev, A. On first-order elliptic systems with two variables that are degenerate on the boundary 576 Eremin, I. I. Symmetric duality for sequential linear programming problems... 581 Kapustin, N. Yu. and Sabitov, K. B. On the solution of a problem in the theory of the Frankl’ problem for equations of mixed type 584 Karatsuba, A. A. Zeros of linear combinations of Z-functions corresponding to Dirichlet series 589 Martynyuk, A. A. On boundedness of solutions of nonlinear systems with small perturbations 591 Salakhitdinov, M. S. and Urinov, A. K. Problems of Bitsadze-Samarskii type for an equation of mixed type 595 Beklaryan, L. A. An optimal control problem for systems with deviating argument, and its connection with the finitely generated group of homeomorphisms of R generated by the deviation functions 600 Dzhuraev, A. On the theory of elliptic systems in multiply connected domains in the plane 606 Zubov, V. I. The structure of the topological transformation determined by a system of differential equations Nguen Khong Tkhai [Nguyen Hong Thai] The theory of semimodules of in- frasemiunits in ideal spaces of vector-valued functions, and its applications to integral operators Stepanov, V. D. On integral operators on the cone of monotone functions, and on imbeddings of Lorentz spaces Sternin, B. Yu. and Shatalov, V. E. On a formula for the asymptotic expansion of an integral in complex analysis Shcherbina, N. V. On the polynomial hull of a two-dimensional sphere in C? .. 628 Table of Contents for the next issue (Vol. 43, No. 3, November—December 1991, Russian original Tom 318, nos. 1-6) Volume 43, Number 3 November-December 1991 CONTENTS Aizenshtat, A. V., Karlovich, Yu. I., and Litvinchuk, G. S. On the defect numbers of the Kveselava-Vekua operator with discontinuous derivative of the shift. 633 Budaev, V. D. On the Bessel inequality for systems of root functions of differential operators 639 Gromov, V. P. Criteria for convergence of an exponential series in function spaces 644 Dzhuraev, A. On some mixed problems for hyperbolic systems of first order... . 648 Zubov, V. I. Interpolation of systems of differential equations 653 Korobov, V. I. and Sklyar, G. M. The method of generating functions for a moment problem with periodic gaps 657 Magaril-Il’yaev, G. G. Average dimension and widths of function classes on the 661 Nasibov, F. G. Extremal problems for polynomials 665 Trubin, V. A. The homogeneity deficit of a network and its reduction 670 Fesenko, I. B. Multidimensional local class field theory 674 Anikonov, Yu. E. and Stepanov, V. N. An inversion formula in a problem of integral geometry 678 Antonevich, A. B. and Radyno, Ya. V. On a general method for constructing algebras of generalized functions 680 Denisov, V. N. On stabilization of the solution of the Cauchy problem for the iterated heat equation 685 Zubov, V. I. Synthesis of multiprogrammed stable controls 689 Karatsuba, E. A. On fast computation of transcendental functions 693 Maksudov, F. G. and Mardanov, I. Dzh. Reduction of a system of linear difference equations in a Banach space 695 Osilenker, B. P. The generalized shift operator with respect to orthogonal matrix polynomials Fedotov, A. M. Numerical algorithms for analytic continuation from discrete sets, and algorithmic proof of uniqueness theorems 701 Kheifits, A. I. Removable sets, regular boundary points, and the Poisson-Jensen formula for generalized subharmonic functions 705 Bochkarev, S. V. Rearrangements of multiplicative systems 708 Bryuno, A. D. On finitely smooth linearization of a system of differential equations near a hyperbolic singular point 711 Gavrilenko, Yu. V. Majorants of logical computations. Lemmas on lifting and descending in logic programming 716 Gurvich, V. A. Criteria for repetition-freeness of functions in the algebra of logic 721 Zubov, V. I. High-frequency excitation of oscillations in the low-frequency range 727 Peshkichev, Yu. A. Moduli of families of two-dimensional surfaces, and quasi- conformal mappings in four-dimensional space 730 Pokornyi, Yu. V. and Karelina, I. G. On the Green function of the Dirichlet problem on a graph 732 Shelukhin, V. V. On the solution of linear evolution equations by a variational 735 Antontsev, S. N. and Shmarév, S. I. The local energy method and vanishing of weak solutions of nonlinear parabolic equations 738 Buyarov, V. S. Logarithmic asymptotics of polynomials orthogonal on the real 743 Vorob’ev, O. Yu. Set-summation 747 Gavrilenko, Yu. V. The structure of principal logical computations and the decomposition of idempotents 752 Gel’fand, I. M., Graev, M. I., and Retakh, V. S. Reduction formulas for hyper- geometric functions on the Grassmannian G;,», and a description of hyper- geometric functions on strata of small codimensions Ershov, Yu. L. Projective T-groups Zubov, V. I. Integrators of differential equations Makarov, V. L. and Khlobystov, V. V. On the general structure of polynomial functional interpolants Martynyuk, A. A. A theorem on multistability Napalkov, V. V. and Bashmakov, R. A. Concerning sufficient sets on algebraic Riemann surfaces Pokhozhaev, S. I. On integral solutions of quasilinear elliptic equations Roitberg, Ya. A. Boundary value and mixed problems for general hyperbolic systems in a complete scale of Sobolev-type spaces Sadovnichii, V. A. and Dubrovskii, V. V. A formula for the first regularized trace of the Laplace-Beltrami operator with a potential Sviridyuk, G. A. Semilinear equations of Sobolev type with relatively bounded operator Strugov, Yu. F. On the homeomorphic nature of some classes of spatial p-harmonic mappings