Investigations in the theory of the approximation of analytic functions carried out at the Mathematics Institute, Academy of Sciences of the Ukrainian SSR

G. A. Alibekov, An Inverse Theorem Concerning the Approximation of Functions of Several Complex Variables [in Russian], First Young Mathematicians Congress of the Republic, No. II, Mathematics Institute of the Academy of Sciences, Ukrainian SSR, Kiev (1965).Google Scholar

G. A. Alibekov, Direct Theorems Concerning the Approximation of a Class of Functions of Several Complex Variables [in Russian], Second Young Ukrainian Mathematicians Congress, Kiev (1966).Google Scholar

S. Ya. Al'per, Uniform Approximation of Functions of a Complex Variable in Closed Regions, Izv. AN SSSR, Ser. Matem.,19 (1955).Google Scholar

S. Ya. Al'per, Mean Approximation of Analytic Functions of the Class E_p [in Russian], in: Contemporary Problems in the Theory of Functions of a Complex Variable, Fizmatgiz, Moscow (1960).Google Scholar

M. I. Andrashko, Mean Approximation of Analytic Functions in Regions with Smooth Boundaries [in Russian], Problems of Mathematical Physics and Function Theory, Izd. Akad. Nauk UkrSSR, Kiev (1963).Google Scholar

M. I. Andrashko, Inequalities for the Derivative of an Algebraic Polynomial in the L_p-Metric(p≥1) in Regions with Angular Points, Ukrainsk. Matem. Zh.,16, No. 4 (1964).Google Scholar

P. É. Antonyuk, Inverse Theorems Concerning the Uniform Approximation of Functions Continuous on Closed Sets, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 9 (1968).Google Scholar

K. I. Babenko, Best-Possible Approximations for a Class of Analytic Functions, Izv. Akad. Nauk SSSR, Ser. Matem.,22, No. 5 (1958).Google Scholar

V. I. Belyi, Problems in the Approximation of Some Classes of Functions Given in a Region of the Complex Plane, Ukrainsk. Matem. Zh.,17, Nos. 1 and 2 (1965).Google Scholar

V. I. Belyi, Inequalities for Derivatives of Fractional Positive Order of Polynomials Given in Regions with Angular Points [in Russian], Trans. of the First Congress of Young Scientists of the Republic, Academy of Sciences of the Ukrainian SSR Press, Kiev (1964).Google Scholar

V. I. Belyi, Constructive Properties of Some Classes of Analytic Functions Given in Regions with Angular Points [in Russian], Trans. of the First Congress of Young Scientists of the Republic, Izd. Akad. Nauk UkrSSR, Kiev (1964).Google Scholar

On Some Properties of a Functional Derivative in a Complex Domain and Their Application to the Theory of Approximation of Functions, Dokl. Akad. Nauk UkrSSR, No. 3 (1965).Google Scholar

On the Constructive Properties of Certain Classes of Functions, Continuous in Regions with Angles, Dokl. Akad. Nauk, Ser. A, No. 2 (1962).Google Scholar

D. L. Berman, Linear Polynomial Operations in a Complex Region and Faber Polynomials, Dokl. Akad. Nauk SSSR,178, No. 2 (1968).Google Scholar

S. N. Bernshtein, Inequalities for Derivatives of Polynomials [in Russian], Collected Works, Vol. 1, Akad. Nauk SSSR (1952).Google Scholar

Yu. A. Brudnyi, Approximations by Entire Function in Regions Exterior to a Segment and to a Semiaxis, Dokl. Akad. Nauk SSSR,124, No. 4 (1959).Google Scholar

Yu. A. Brudnyi, A Method of Approximating Bounded Functions Defined on a Segment [in Russian], in: Contemporary Problems in Constructive Function Theory, Baku (1965).Google Scholar

Yu. A. Brudnyi, Approximation of Functions by Algebraic Polynomials, Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 4 (1968).Google Scholar

S. A. Verbanov, Averaged Interpolation Polynomials and Polynomial Operations in the Complex Plane [in Russian], Review by the Author of his Dissertation, Leningrad (1968).Google Scholar

Yu. I. Volkov, Some Problems in the Approximation of Functions of a Complex Variable in Regions with Angular Points [in Russian], First Congress of Young Mathematicians of the Republic, No. 2, Mathematics Institute of the Academy of Sciences, UkrSSR, Kiev (1965).Google Scholar

Yu. I. Volkov, Constructive Characteristics of Functions of a Complex Variable in Regions with Piecewise-smooth Boundaries, Ukrainsk. Matem. Zh.,17, No. 3 (1965).Google Scholar

Yu. I. Volkov, Boundary Values of a Class of Functions Analytic in a Disk, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 11 (1968).Google Scholar

M. M. Vorobiov, Approximation of Analytic Functions by Partial Sums of Faber Series, Dokl. Akad. Nauk UkrSSR, No. 2 (1966).Google Scholar

M. M. Vorobiov, A Note Concerning V. K. Dzyadyk's Theorem on the Approximation of Functions of the Class W^rH^α, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1 (1967).Google Scholar

N. N. Vorob'ev, Approximation of Continuous Functions of Classes Defined on Jordan Arcs, Ukrainsk. Matem. Zh.,19, No. 3 (1967).Google Scholar

N. N. Vorob'ev, Simultaneous Approximation of Functions and Their Derivatives in a Region of the Complex Plane, Ukrainsk. Matem. Zh.,20, No. 1 (1968).Google Scholar

N. N. Vorob'ev and R. V. Polyakov, The Constructive Character of Continuous Functions Defined on Smooth Arcs, Ukrainsk. Matem. Zh.,20, No. 6 (1968).Google Scholar

D. M. Galan, Approximation of Functions of a Complex Variable Defined in Closed Regions with Angular Points by Polynomials, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 11 (1967).Google Scholar

D. M. Galan, Mean Approximation of Regular Functions of the Class E₁ in Regions with Smooth Boundaries, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 8 (1967).Google Scholar

G. M. Goluzin, The Geometrical Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).Google Scholar

I. E. Gopengauz, Problems in the Approximation of Functions on a Segment and in Regions with Angular Points [in Russian], Theory of Functions, Functional Analysis and Their Applications, No. 4, Khar'kov Un-ta (1967).Google Scholar

V. K. Dzyadyk, The Constructive Character of Functions Satisfying a Lip α condition (0 < α < 1) on a Finite Segment of the Real Axis, Izv. Akad. Nauk SSSR, Ser. Matem.,20, No. 5 (1956).Google Scholar

V. K. Dzyadyk, A Further Strengthening of Jensen' s Theorem on the Approximation of Continuous Functions by Algebraic Polynomials, Dokl. Akad. Nauk SSSR,121, No. 3 (1958).Google Scholar

V. K. Dzyadyk, Approximation of Functions by Ordinary Polynomials on a Finite Segment of the Real Axis, Izv. Akad. Nauk SSSR, Ser. Matem.,22, No. 3 (1958).Google Scholar

V. K. Dzyadyk, S. M. Nikol'skii's Problem in a Region of the Complex Plane, Izv. Akad. Nauk SSSR, Ser. Matem.,23 (1959).Google Scholar

V. K. Dzyadyk, Inverse Theorems in the Approximation of Functions in Regions with Angular Singularities, Dokl, Akad. Nauk SSSR,127, No. 3 (1959).Google Scholar

V. K. Dzyadyk, The Approximation of Continuous Functions in Closed Regions with Angular Points and S. M. Nikol'skii's Problem (First Communication), Izv. Akad. Nauk SSSR, Ser. Matem.,26, No. 6 (1962).Google Scholar

V. K. Dzyadyk, Inverse Theorems in the Approximation of Functions in Complex Regions, Ukrainsk. Matem. Zh.,15, No. 4 (1963).Google Scholar

V. K. Dzyadyk, Some Theorems on the Transformation and Approximation of Analytic Functions, Dokl. Akad. Nauk SSSR,151, No. 2 (1963).Google Scholar

V. K. Dzyadyk, A Contribution to the Theory of Approximation of Analytic Functions Continuous in Closed Regions and S. M. Nikol'skii's Problem (Second Communication), Izv. Akad. Nauk SSSR, Ser. Matem.,27, No. 5 (1963).Google Scholar

V. K. Dzyadyk, Approximation of Functions of H^ω in Closed Regions by Polynomials [in Russian], in: Contemporary Problems in Constructive Function Theory, Baku (1965).Google Scholar

V. K. Dzyadyk, The Constructive Character of Functions of Holder Classes [in Russian], in: Contemporary Problems in Analytic-Function Theory, Nauka, Moscow (1966).Google Scholar

V. K. Dzyadyk, The Approximation of Analytic Functions in Regions with Smooth and Piecewise-Smooth Boundaries [in Russian], Third Annual Mathematical School, Naukova Dumka, Kiev (1966).Google Scholar

V. K. Dzyadyk, Analytic and Harmonic Transformations of Functions and the Approximation of Harmonic Functions, Ukrainsk. Matem. Zh.,19, No. 5 (1967).Google Scholar

V. K. Dzyadyk, The Constructive Character of Functions of Hölder Classes on Closed Sets with Piecewise-Smooth Boundaries with Possible Angular Points with Zero Angles, Ukrainsk. Matem. Zh.,20, No. 5 (1968).Google Scholar

V. K. Dzyadyk and G. A. Alibekov, The Uniform Approximation of Functions of a Complex Variable on Closed Sets with Angular Points, Matem. Sb.,75 (117), No. 4 (1968).Google Scholar

V. K. Dzyadyk and D. M. Galan, Approximation of Analytic Functions in Regions with Smooth Boundaries, Ukrainsk. Matem. Zh.,17, No. 1 (1965).Google Scholar

V. K. Dzyadyk and R. N. Koval'chuk, Interpolation of Functions of Several Complex Variables [in Russian], in: Problems in Mathematical Physics and Function Theory, Naukova Dumka, Kiev (1965).Google Scholar

V. K. Dzyadyk and O. I. Shvay, “On the Constructive Characteristic of Functions of the Hölder Classes in Regions with a Fragmental-Smooth Boundary and Arbitrary Additional External Angles,” Dokl. Akad. Nauk, Ser. A, No. 2 (1962).Google Scholar

P. Ya. Kiselev, The Approximation of Analytic Functions by Polynomials in a Finite Number of Regions, Ukrainsk. Matem. Zh.,14, No. 2 (1962).Google Scholar

P. Ya. Kiselev, Some Problems in the Approximation of Analytic Functions in a Finite Number of Regions [in Russian], in: Contemporary Problems in Constructive Function Theory, Baku (1965).Google Scholar

R. M. Koval'chuk, Direct Theorems Concerning the Approximation of Analytic Functions of Several Complex Variables in Semicylindrical Regions, Dokl. Akad. Nauk UkrSSR, No. 2 (1965).Google Scholar

R. N. Koval'chuk, A Generalization of Kellog's Theorem, Ukrainsk. Matem. Zh.,17, No.4 (1965).Google Scholar

R. N. Koval'chuk, The Approximation and Interpolation of Functions of Several Complex Variables [in Russian], Trans. of the Scientific Conference of Engineers, Graduate Students, and Members of the Mathematics Institute of the Academy of Sciences, UkrSSR, Izd-vo Akad. Nauk UkrSSR, Kiev (1963).Google Scholar

R. N. Koval'chuk, Moduli of Continuity of Functions Defined in Closed Disks [in Russian], Trans. of the First Congress of Young Scientists of the Republic, Naukova Dumka, Kiev (1965).Google Scholar

L. I. Kolesnik, The Approximation of Functions Continuous on Jordan's Arcs, Ukrainsk. Matem. Zh.,19, No. 2 (1967).Google Scholar

N. A. Lebedev, Inverse Uniform Approximation Theorems, Dokl. Akad. Nauk SSSR,171, No. 4 (1966).Google Scholar

N. A. Lebedev and P. M. Tamrazov, Inverse Approximation Theorems for Closed Sets in the Complex Plane, Dokl. Akad. Nauk SSSR,179, No. 5 (1968).Google Scholar

G. K. Lebed', Inequalities for Polynomials and Their Derivatives, Dokl. Akad. Nauk SSSR,117, No. 4 (1957).Google Scholar

V. N. Malozemov, Simultaneous Approximation of Functions and Their Derivatives by Algebraic Polynomials, Dokl. Akad. Nauk SSSR,170, No.4 (1966).Google Scholar

A. I. Markushevich, Faber Polynomials, Izv. Akad. Nauk SSSR, Ser. Matem.,8, No. 1 (1944).Google Scholar

S. N. Mergelyan, Some Problems in Constructive Function Theory [in Russian], Trans. of the V. A. Steklov Mathematics Institute, Vol. 37, Moscow (1951).Google Scholar

N. I. Muskhelishvili, Singular Integral Equations [in Russian], Fizmatgiz, Moscow (1962).Google Scholar

S. M. Nikol'skii, The Approximation of Functions of Several Variables by Polynomials [in Russian], Trans. of the Third All-Union Mathematics Congress, Vol. 3 (1960).Google Scholar

S. M. Nikol'skii, Best-Possible Polynomial Approximations of Functions Satisfying a Lipschitz Condition, Izv. Akad. Nauk SSSR, Ser. Matem.,10 (1946).Google Scholar

I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow-Leningrad (1950).Google Scholar

V. I. Smirnov and N. A. Lebedev, The Constructive Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow-Leningrad (1964).Google Scholar

S. A. Telyakovskii, Two Theorems Concerning the Approximation of Functions by Algebraic Polynomials, Matem. Sb.,70 (112), No. 2 (1966).Google Scholar

A. F. Timan, An Improvement of Jensen's Theorem Concerning the Best-Possible Polynomial Approximation of Continuous Functions on a Finite Segment of the Real Axis, Dokl. Akad. Nauk SSSR,78, No. 1 (1951).Google Scholar

A. F. Timan, Inverse Theorems in the Constructive Theory of Functions Given on a Finite Segment of the Real Axis, Dokl. Akad. Nauk SSSR,116, No. 5 (1951).Google Scholar

R. M. Trigub, Approximation of Functions by Polynomials with Integral Coefficients, Izv. Akad. Nauk SSSR, Ser. Matem.,26, No. 2 (1962).Google Scholar

A. I. Shvai, An Improvement in the Order of Approximation of Functions Given in Regions with Angular Points in Neighborhoods of Angular Points, Ukrainsk. Matem. Zh.,19, No. 4 (1967).Google Scholar

G. Freud, Über die Approximation reller stetigen Funktionen durch gewöhnliche Polynome, Math. Ann.,137, No. 1, 17–25 (1959).Google Scholar

G. H. Hardy and J. E. Littlewood, Some Properties of Fractional Integrals, I and II, Math. Zeitschr.,27, 565–606 (1928); Math. Zeitschr.,34, 403–439 (1932).Google Scholar

Heuzer, Zur Theorie der Faberschen Polynomreihen, Deutsch. Math., H.4 (1939).Google Scholar

W. E. Sewell, Degree of Approximation by Polynomials in Complex Domains, Annals of Math. Studies,9, Princeton (1942).Google Scholar

G. Szegö, Über einen Satz von A. Markoff, Math. Zeitschr.,23, 45–61 (1925).Google Scholar

G. Szegö and A. Zygmund, On Certain Mean Values of Polynomials, J. Analyse Math.,3, 225–244 (1954).Google Scholar

J. L. Walsh and H. M. Elliott, Polynomial Approximation to Harmonic and Analytic Functions; Generalized Continuity Conditions, Trans. Amer. Mathem. Soc.,68, No. 2, 183–203 (1958).Google Scholar

D. W. Western, Inequalities of the Markoff and Bernstein Type for Integral Norms, Duke Mathem. J.,15, No.3 (1948).Google Scholar