Generalization of weierstrass canonical integrals

• Autorzy: Olga Veselovska
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove that a subharmonic function in ℝm of finite λ-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of finite λ-type which tends to zero uniformly on compacts of ℝm. The known Brelot-Hadamard representation of subharmonic functions in ℝm of finite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of λ-admissible mass distributions are investigated.

Słowa kluczowe

EN

Subharmonic function; Weierstrass canonical integral; Brelot-Hadamard representation; subharmonic function of finite λ-type; 31B05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 4
• Strony: 593-604

Daty

wydano

2004-08-01

online

2004-08-01

Twórcy

autor

Olga Veselovska

• National University “Lviv Polytechnica”,

Bibliografia

• [1] L.I. Ronkin: Introduction into the theory of entire functions of several variables, Nauka, Moscow, 1971. [Russian]
• [2] A. Bateman, A. Erdelyi: Higher transcendental functions, 2, Nauka, 1974. [Russian]
• [3] W.K. Hayman, R.B. Kennedy: Subharmonic functions, Acad. Press, London, 1976.
• [4] A.A. Kondratyuk: “Spherical harmonics and subharmonic functions (Russian)”, Mat. Sb., Vol. 125, (1984), pp. 147–166. [English translation in Math. USSR, Sb. 53, (1986), pp. 147–167]
• [5] B. Azarin: Theory of growth of subharmonic functions, Texts of lecture, part 2, Krakov, (1982). [Russian]
• [6] vL.A. Rubel: A generalized canonical product In trans: Modern problems of theory of analytic functions, Nauka, Moscow (1966), pp. 264–270.
• [7] Ya. V. Vasylkiv, An investigation asymptotic characteristics of entire and subharmonic functions by method of Fourier series, Abstract dissertation, Donetsk, 1986. (Russian)
• [8] E. Stein, G. Weiss: Introduction to Fourier analysis of Euclidean spaces, Princeton University Press, Princeton, New Jersey, 1971.
• [9] H. Berens, P.L. Butzer, S. Pawelke: “Limitierungs verfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten”, Publs. Res. Inst. Math. Sci., Vol. 4, (1968), pp. 201–268.
• [10] A.A. Kondratyuk: “On the method of spherical harmonics for subharmonic functions (Russian)”, Mat. Sb., Vol. 116, (1981), pp. 147–165. [English translation in Math. USSR, Sb. 44, (1983), pp. 133–148]
• [11] O.V. Veselovska: “Analog of Miles theorem for δ-subharmonic functions in ℝm ”, Ukr. Math. J., Vol. 36, (1984), pp. 694–698. [Ukrainian]
• [12] N.N. Lebedev: Special functions and their applications, Revised edition, translated from the Russian and edited by Richard A. Silverman, Dover Publications, Inc., New York, 1972.
• [13] L.I. Ronkin: Functions of completely regular growth, translated from the Russian by A. Ronkin and I. Yedvabnik, Mathematics and its Applications (Soviet Series), Vol. 81, Kluwer Academic Publishers Group, Dordrecht, 1992.

Identyfikatory

DOI

10.2478/BF02475966