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

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• [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]
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Identyfikatory

DOI

10.2478/BF02475966