Levan Zhizhiashvili

Date of Birth: 1934

In 1961 he defended his candidate theisis at A.Razmadze Institute of Mathematics and in 1967 at Moscow State University he defended his doctoral thesis. Since 1968 he fills a position of professor (scientific title - proffessor), and since 1978 he is the head of the chair of the function theory and functional analysis at Tbilisi State University.In 1974 he was elected a Corresponding Member of  Georgian Academy of Sciences, and since 1993 he is an Academician of the same Academy.
L. Zhizhiashvili is well-known specialist of the function theory and functional analysis. He is the author of more than 65 works, including 4 monographs.

He solved:
a) the problem of A. Zygmund and P. L. Ulyanov concerning the almost everywhere existence of conjugate functions and Hilbert transforms of several variables;
b) the problem of D.E. Menshov on the convergence in measure of Cesaro and Abel-Poisson means of multiple conjugate series.

He established:
a) most general estimates ( both in one and multi- dimension cases) for approximations by Cesaro means of Fourier series of continuous functions as well as of the functions which are Lebesgue integrale with the power greatel or equal to 1;
b) thge connection of approximate properties of the above mentioned means with Hardy-Littlewood Nikolskii imbedding theorems.

He proved that:
a) multidimensional Hilbert operator does not possess a weak type inequality even on the intersection of all the Lebesgue classes with powers greater or equal to 1;
b) (multidimrnsional complex analysis) if for a logarithm-scaled Lebesgue space the power of the logarithm is less than dimension minus1 , then for a density from this space, the multiple Schwarz integral may have no boundary value almost everywhere.

The contributions of L. Zhizhiashvili in educating young scientists is considerable. Among his pupils there are 7 doctors of sciences and more then 20 candidates.
L. Zhizhiashivli is a university prize laureat. He is a member of various societies, he is a Honoured Scientist, was awarded the Order of Red Banner of Labour.
L. Zhizhiashvili carries out many-sided scientific, pedagogic and organizatory activities. He was the Dean of the Department of Mechanics and Mathematics, he guids the publishing of the proceedings of the Scientific seminar led by himself. During many years he was the chairman of a Specialized Doctor Council.

Publications:

• Conjugate functions of two variables and double Fourier series(Russian) Dokl. Akad. Nauk SSSR, 149 (1963), N 4, pp. 765-768.
• Conjugate functions of two variable and double conjugate trigonometric series (Russian),Dokl. Acad. Nauk SSSR, 155 (1964),N 3 pp.521-523.
• Some properties of (C,alpha)-means of fourier series and conjugate trigonometric series (Russian), Mat. Sbornic,63, (1964), N.4, pp.489-504.
• On some properties of Cesaro means of Fourier series (Russian),Uspekhi Mat. Nauk. 21, (1966) N 1, pp. 171-174.
• On some properties of Cesaro means of Fourier series,(Russian),Trudy Moskov. Mat. Obshch. 15, (1966) pp. 145-180.
• On conjgate functions (Russian)Dokl. Akad. Nauk SSSR, 167,(1966)N 2, pp.278-281; English translation:Soviet. Math. Dokl., 7 (1966), pp.368-371.
• Generalization of a theorem of Marcinkiewicz (Russian), Izv. Akad. Nauk SSSR, Ser. Math., 32 (1968), N 3, pp.269-280.
• Generalization of a theorem of Riesz to the case of several variables (Russian), Mat. Zametki, 4 (1968), N 3, pp. 269-280.
• Conjugate functions and trigonometric series (Russian), Tbilisi State Univ., Tbilisi, (1969).
• Some problems in the theory if simple and multiple trigonometric and orthogonal series (Russian), Uspekhi Mat. Nauk, 28 (1973), N.2, pp.65-119; English translation: Russian Math. Syrveys, 28 I1973), N. 2, pp. 65-127.
• Conjugate of a variables (Russian), Dokl. Akad. Nauk SSSR, 218 (1974), N.3, pp. 517-518 English translation: Sovet Math. Dokl., 15 (1974), pp. 1372-1373.
• Trogonometric Fourier series (Russian), Mat. Sbornik, 100 (1976), N.4, pp.580-609.
• Validity of A. N. Kolmogorov's theorem for conjugate functions of several variables (Russian), Mat. Zametki, 32 (1982), N. 1 pp. 13-21.
• On some approximating properties of Casaro means of Fourier series (Russian), Dokl, Akad. Nauk SSSR, 269 (1983), N. 6, pp. 1307-1309.
• Conjugate functions of several variables and multiple conjugate trigonometric series (Russian), Dokl.Akad. Nauk SSSR, 284 (1985), N. 1, pp. 34- 35.
• Solution of a problem of D. E. Menshov (Russian), Dokl. Akad. Nauk SSSR, 320(1991), N. 2, pp.273-274; English translation; Soviet Math. Dokl.,44(1992), N. 2, pp. 427-429.
• On almost everywhere summation of multiple conjugate trigonometric series (Russian), Dokl. Akad. Nauk SSSR, 320 (1991). N.3 pp. 529-530; English translation: Soviet Math. Dokl., 44 (1992), N.2, pp. 471- 473.
• v 18. Some problem of multidimensional harmonic analysis, second edition (Russian), Tbilisi State University,Tbilisi,(1996).
• Trigonomnetric fourier series and their conjugates. Kluwer Academic Publishers, Dodrechi, Soston, London, 1996.

|Structure| |Presidium| |Institutes| |Members| |Publications| |Events at GAS| |Search the Site| |Collection of Links|