Selected works on the theory of functions and mathematical physics. Vol. 2 (Q2783462)

To this volume of two-volume book of selected works by the famous mathematician \textit{Naum Illich Akhiezer} (1901--1980) there are included publications which developed the theory of approximation of continuous functions by polynomials or by entire functions of exponential type. A special role of papers on the theory of orthogonal polynomials and their continuum analogues should be noted. These papers are that basis on which theory of integrable nonlinear equations was developed. The publications included are as follows:NEWLINENEWLINEOn an application of the H. Bohr and J. Favard inequality (with B. M. Levitan). [Dokl. Akad. Nauk SSSR 14, No. 7, 419--421 (1937; Zbl 0016.30002)],NEWLINENEWLINEOn best approximation of differentiable periodic functions by trigonometric sums (with M. G. Krein). [Dokl. Akad. Nauk SSSR 15, No. 3, 107--111 (1937; Zbl 0016.30001)],NEWLINENEWLINEOn best approximation of a class of continuous periodic functions. [Dokl. Akad. Nauk SSSR 17, No. 9, 455--457 (1937; Zbl 0018.01304)],NEWLINENEWLINEOn interpolation of entire transcendental functions of finite degree. [Dokl. Akad. Nauk SSSR, N. Ser. 65, 781--784 (1949; Zbl 0036.18602)],NEWLINENEWLINEOn interpolation of entire transcendental functions of finite degree (with B. Ya. Levin). [Zapiski Kharkovsk. Mat. Obshch., (4) 23, No. 4, 5--26 (1952)],NEWLINENEWLINEOn entire transcendental functions of finite degree which have majorant on a sequence of real points. [Izv. Akad. Nauk SSSR, Ser. Mat. 16, 353--364 (1952; Zbl 0049.32901)],NEWLINENEWLINEOn weak weight functions. [Dokl. Akad. Nauk SSSR, N. Ser. 93, 949--952 (1953; Zbl 0051.30101)],NEWLINENEWLINEOn weighted approximation of continuous functions by polynomials on the real axis. [Usp. Mat. Nauk 11, No. 4(70), 1--43 (1956; Zbl 0071.05801)],NEWLINENEWLINEA generalization of the S. Bernstein inequality for derivatives of entire functions (with B. Ya. Levin). [Issledovaniya po Sovremennym Problemam Teorii Functsij Kompleksnogo Peremennogo. Moskva Fizmatgiz, 111--165 (1960)],NEWLINENEWLINEOn polynomials orthogonal on a circular arc. [Sov. Math., Dokl. 1, 31--34 (1960); translation from Dokl. Akad. Nauk SSSR 130, 247--250 (1960; Zbl 0129.28305)],NEWLINENEWLINEOrthogonal polynomials on several intervals. [Sov. Math., Dokl. 1, 989--992 (1960); translation from Dokl. Akad. Nauk SSSR 134, 9--12 (1960; Zbl 0101.29205)],NEWLINENEWLINEOn the theory of orthogonal polynomials over several intervals (with Yu. Ya. Tomchuk). [Sov. Math., Dokl. 2, 687--690 (1961); translation from Dokl. Akad. Nauk SSSR 138, 743--746 (1961; Zbl 0109.29601)],NEWLINENEWLINEA continuous analogue of orthogonal polynomials on a system of intervals. [Sov. Math., Dokl. 2, 1409--1412 (1961); translation from Dokl. Akad. Nauk SSSR 141, 263--266 (1961; Zbl 0109.29602)],NEWLINENEWLINEA continuous analogue of polynomials orthogonal on a circular arc. [Sov. Math., Dokl. 2, 1526--1529 (1961); translation from Dokl. Akad. Nauk SSSR 141, 769--772 (1961; Zbl 0125.31303)],NEWLINENEWLINEA continuum analogue of some theorems on Toeplitz matrices. [Ukr. Mat. Zh. 16, 445--462 (1964; Zbl 0154.37202)],NEWLINENEWLINEOrthogonal polynomials on a system of intervals and their continuum analogue. [Tr. IV Vsesoyuz. Mat. S'ezda, Leningrad 1961, 2, 623--628 (1964; Zbl 0196.44404)],NEWLINENEWLINEOn continuum analogues of orthogonal on a circle polynomials (with A. M. Rybalko). [Ukr. Mat. Zh. 20, No. 1, 3--24 (1968; Zbl 0169.46601)],NEWLINENEWLINEOn one indeterminate equation of Chebyshev type in the problem of construction of orthogonal systems. [Mat. Fiz. Funkt. Anal. 2, 3--14 (1971)],NEWLINENEWLINEOn some inversion formuale for singular integrals. [Izv. Akad. Nauk SSSR, Ser. Mat. 9, 275--290 (1945; Zbl 0060.25905)],NEWLINENEWLINEOn a generalization of the Fourier transformation and Paley-Wiener theorem. [Dokl. Akad. Nauk SSSR, n. Ser. 96, 889--892 (1954; Zbl 0057.09203)],NEWLINENEWLINEOn the diffraction of electromagnetic waves at a circular hole in a flat screen (with A. N. Akhiezer). [Dokl. Akad. Nauk SSSR 109, 53--56 (1956; Zbl 0072.43701)],NEWLINENEWLINETo the theory of paired integral equations. [Zap. Kharkov. Mat. Obshch., Ser. 4, 25, 5--31 (1957)],NEWLINENEWLINEEffective boundary condition on the boundary surface of multiplicative and decelerating medium (with A. I. Akhiezer and G. Ya. Lyubarskij). [Zh. Tekhn. Fiz. 27, No. 4, 822--829 (1957)],NEWLINENEWLINEOn inversion of some singular integrals (with V. A. Shcherbyna). [Zap. Kharkov. Mat. Obshch., Ser. 4, 25, 191--198 (1957)],NEWLINENEWLINESome inversion formulas. [Zap. Kharkov. Mat. Obshch., Ser. 4, 27, 91--95 (1961)],NEWLINENEWLINEOn one Sturm-Liouville equation on semi-axis. [Zap. Kharkov. Mat. Obshch. Ser. 4, 29, 44--52 (1963)],NEWLINENEWLINEOn the Lamé equation. [Zap. Kharkov. Mat. Obshch. Ser. 4, 30, 5--17 (1964)],NEWLINENEWLINEOn spectral theory of the Lamé equation. [Istor.-Mat. Issled. 23, 77--86 (1978; Zbl 0423.34031)],NEWLINENEWLINEOn separate-analytical functions of several variables and `acute wedge' theorems (with L. I. Ronkin). [Usp. Mat. Nauk 28, No. 3, 27--42 (1973; Zbl 0284.32009)],NEWLINENEWLINEOn separate-analytical functions of several variables (with L. I. Ronkin). [CA] Quest. math. Phys. Funct. Anal., Mater. Sci. Semin., Phys.-Tech. Inst. Low Temp. Acad. Sci. Ukr. SSR, Kiev, 3--10 (1976; Zbl 0428.32001)],NEWLINENEWLINESome inverse problems of spectral analysis connected with hyper-elliptic integrals. From the book by \textit{N. I. Akhiezer} and \textit{I. M. Glazman} [Theory of linear operators in Hilbert space. Kharkov: Vyshcha Shkola, V. 2, 242--283 (1978)],NEWLINENEWLINEOn construction a flow that are flowing around thin profile. [Zb. Pr. Inst. Mat. AN URSR, No. 4, 151--156 (1940)],NEWLINENEWLINEThe Markov moment problem with respect to arbitrary number of intervals. [Ukr. Mat. Zh. 1, No. 3, 41--50 (1949; Zbl 0049.19905)],NEWLINENEWLINEOn weighted approximation continuous on the real axis functions by polynomials (with K. I. Babenko). [Dokl. Akad. Nauk SSSR, N. Ser. 57, 315--318 (1947; Zbl 0029.02704)].