Abstract
In this paper we shall briefly review the main facts referring to majorants (Perron envelopes) of special classes of functions, which are subharmonic in ℂ, and describe some applications of the majorants.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akhiezer N.I. and Levin B. Ja. Generalizations of the Bernstein inequalities for derivatives of entire functions. In: “Studies in the Modern Problems of the Theory of Functions of a Complex Variable”. Moscow, Fiz-matgiz, 1960, pp. 125–183 (in Russian).
Levin B. Ja. Subharmonic majorants and their applications. In: Abstracts of the All-Union Conference on the Theory of Functions, 1971, Kharkov, FTINT AN Ukr. SSR, pp. 117–120.
Levin B. Ja. On some special conformai mappings. In: “Problems of Mathematics”, coll. of papers No. 510, Tashkent, 1976, pp. 140–147 (in Russian).
Levin B. Ja. Extremal problem in classes of subharmonic functions and their applications. Constructive theory of functions-84. Sofia, 1984, pp. 534–543.
Levin B. Ja. Majorants in classes of subharmonic functions and their applications. I. Preprint No. 18–84, FTINT AN Ukr. SSR, Kharkov 1984, pp. 1–52 (in Russian).
Levin B. Ja. Majorants in classes of subharmonic functions and their applications. II. Preprint No. 19–84, FTINT AN Ukr. SSR, Kharkov 1984, pp. 1–34 (in Russian).
Levin B. Ja. Completeness of a system of functions, quasi-analyticity and subharmonic majorants. Proc. of Steklov Inst. (Leningrad Department). Studies in the Linear Operator Theory and Function Theory, to appear.
Koosis P. Fonctions entières de type exponentiel comme multiplicateurs. Un exemple et une condition nécessaire et suffisante. Ann. Scient. Ec. norm, sup., 4 série, t. 16, 1983, pp. 375–407.
Koosis P. La plus petite majorante surharmonique…, Annales de l’Institut Fourier de Grenoble, t. XXXII, Fase. 1, 1983, pp. 67–107.
Beurling A., Malliavin P. On Fourier transforms of measures with compact support. Acta Math., v. 107, 1962, pp. 291–309.
Hayman W.K. Questions of regularity connected with the Phragmén-Lindelöf principle. J. Math. Pures Appl., 1956, v. 35, pp. 115–126.
Azarin V.S. Generalization of a Hayman theorem to subharmonic functions in the n-dimensional cone. Mat. Sb., 1965, v. 66 (108), No. 2, pp. 248–264 (in Russian).
Eremenko A.E. On the entire functions bounded on the real axis. DAN SSSR, 1987 (in Russian).
Pfluger A. Des théorèmes du type de Phragmén-Lindelöf. C.R. Acad. Sci. Paris, t. 229, 1949, pp. 542–543.
Benedicks M. Positive harmonic functions vanishing on the boundary of certain domain in R n. Ark. Math., 1980, v. 18, No. 1, pp. 53–72.
Schaeffer A.C. Entire functions and trigonometric polynomials. Duke Math. J., 1953, v. 20, pp. 77–88.
Katznelson V.E. Equivalent norms in spaces of entire functions of the exponential type. Mat. Sb., 1973, v. 92 (134), No. 1 (9), pp. 34–54 (in Russian).
Levin B. Ja. and Logvinenko V.N. On the classes of the functions, sub-harmonic in R n and bounded on a certain set. In: Proc. of Steklov Inst. (Leningrad Department), Coll. dedicated to Centenary of V.I. Smirnov (in Russian), to appear.
Fryntov A.E. One extremal problem of the potential theorem. DAN SSSR (in Russian), to appear.
Marchenko V.A. and Ostrovski I.V. Characterization of the spectrum of the Hill operator. Mat. Sb., 1975, v. 97 (139), No. 4 (8), pp. 540–606 (in Russian).
Marchenko V.A. and Ostrovski I.V. Approximation of periodic potentials by finite-band ones. Vestnik Kharkovsk. Univ., No. 205. Priklad. Mat. i Mekhan., vyp. 45, 1980 (in Russian).
Kovalenko K.R. and Krein M.G. On certain studies of A.M. Lyapunov in differential equations with periodic coefficients. DAN SSSR, v. XXV, No. 4, 1950, pp. 495–498 (in Russian).
Krein M.G. On inverse problems of the theory of filters and stability λ-bands. DAN SSSR. v. 93, No. 5, 1953, pp. 767–770 (in Russian).
Krein M.G. The main statements of the stability A-bands of the canonical system of linear differential equations with periodic coefficients. A. A. Andronov Memorial Coll., Izd. AN SSSR, 1955, pp. 412–498 (in Russian).
Misyura T.V. Characterization of the spectra of the periodic and an-tiperiodic boundary problems generated by the Dirac operation. I. The theory of functions, functional analysis and applications, 1978, vyp. 30, Kharkov, pp. 94–101; II. The theory of functions, functional analysis and applications, 1979, vyp. 31, Kharkov, pp. 102–109 (in Russian).
II. The theory of functions, functional analysis and applications, 1979, vyp. 31, Kharkov, pp. 102-109 (in Russian).
Mikhailova I.V. The theory of the entire J-dilating matrix functions and its application in inverse problems. Synopsis of a Thesis, Kharkov, 1985 (in Russian).
Kargaev P.P. Existence of the Phragmen-Lindelof function and some conditions of quasi-analyticity. Proc. of Steklov Inst. (Leningrad Department), 1983, v. 126 (in Russian)
Levin B. Ja. Majorants in classes of subharmonic functions. The theory of functions, functional analysis and applications, to appear in N51, Kharkov.
Levin B. Ja. Connection between majorants and conformai mapping. Ibid., to appear in N52, Kharkov.
Levin B. Ja. Classification of closed sets in R and representation of majorants. Ibid., to appear in N52, Kharkov.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Levin, B.J. (1988). Subharmonic Majorants and Some Applications. In: Hersch, J., Huber, A. (eds) Complex Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9158-5_16
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9158-5_16
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-1958-8
Online ISBN: 978-3-0348-9158-5
eBook Packages: Springer Book Archive