Selected works on the theory of functions and mathematical physics. Vol. 1 (Q2783461)

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 polynomials of least deviation from zero created by \textit{P. L. Chebyshev, E. I. Zolotarev} and \textit{A. A. Markov}. In particular, the author found the general form of polynomials of least deviation with given three main coefficients. The publications included are as follows:NEWLINENEWLINEOn some functions of least deviation from zero on given intervals. [Izv. Fiz.-Mat. Ob. Kazan, (3), 3, 1--69 (1928; JFM 57.1430.02)],NEWLINENEWLINEOn polynomials of least deviation from zero [Trudy I Vsesoyuz. Mat. S'ezda, 284--289 (1930)],NEWLINENEWLINEOn exponential properties of some fractional functions [Dokl. Akad. Nauk SSSR, Ser. A 18, 495--499 (1930; JFM 57.1431.02)],NEWLINENEWLINEAsymptotic solution of a problem on polynomials of least deviation [Zap. Khark. Mat. Ob. (4) 4, 141--144 (1930)].NEWLINENEWLINEOn an extremum Chebyshev problem. [Math. Ann. 104, 739--744 (1931; Zbl 0002.03901; JFM 57.0414.03)],NEWLINENEWLINEOn asymptotic properties of some polynomials. [C. R. Acad. Sci. 191, 908--910 (1930; JFM 56.0304.02)],NEWLINENEWLINEOn the asymptotic value of the best approximation of some fractions by polynomials. [C. R. Acad. Sci. 191, 991--993 (1930; JFM 56.0950.04)],NEWLINENEWLINEOn a minimum problem of the theory of functions and a number of roots of algebraic equations inside the unit circle. [Bull. Acad. Sci. URSS, VII. Ser., No. 9, 1169-1189 (1931; Zbl 0003.39103)],NEWLINENEWLINEOn asymptotic value of error of the best approximation of some fractional functions by polynomials. [Zap. Khark. Mat. Ob., (4) 5, 37--49 (1932; Zbl 0004.39202)],NEWLINENEWLINEOn some functions of least deviation from zero on two given intervals. I,II,III. [Bull. Acad. Sci. URSS, VII. Ser. 1932, No. 9, 1163-1202 (1932; Zbl 0007.00802)], [Bull. Acad. Sci. URSS, VII. Ser. 1933, No. 3, 309--344 (1933; Zbl 0007.34106)], [Bull. Acad. Sci. URSS, VII. Ser. 1933, No. 4, 499--535 (1933; Zbl 0007.34201)],NEWLINENEWLINERemarks on extremal properties of some fractions related with transformations of elliptic functions. [Zap. Khark. Mat. Ob. (4), 11, 27--34 (1935; Zbl 0012.15901)],NEWLINENEWLINEOn entire functions of finite degree with least deviation from zero. [Mat. Sb., New Ser. 31(73), 415--438 (1952; Zbl 0049.32902),NEWLINENEWLINEOn a family of entire functions of finite degree and a Chebyshev problem. [Izv. Akad. Nauk SSSR, Ser. Mat. 16, 459--468 (1952; Zbl 0048.04701)],NEWLINENEWLINEOn best weighted approximation on the real line by entire functions of finite degree. [Dokl. Akad. Nauk SSSR, N. Ser. 94, 983--986 (1954; Zbl 0055.29401)],NEWLINENEWLINEExtremal properties of entire functions of exponential type [Teor. Funkts. Funkts. Anal. Prilozh. 1, 111-135 (1965; Zbl 0257.30023)].