# Generalization of weierstrass canonical integrals

Open Mathematics (2004)

- Volume: 2, Issue: 4, page 593-604
- ISSN: 2391-5455

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topOlga Veselovska. "Generalization of weierstrass canonical integrals." Open Mathematics 2.4 (2004): 593-604. <http://eudml.org/doc/268723>.

@article{OlgaVeselovska2004,

abstract = {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.},

author = {Olga Veselovska},

journal = {Open Mathematics},

keywords = {31B05},

language = {eng},

number = {4},

pages = {593-604},

title = {Generalization of weierstrass canonical integrals},

url = {http://eudml.org/doc/268723},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Olga Veselovska

TI - Generalization of weierstrass canonical integrals

JO - Open Mathematics

PY - 2004

VL - 2

IS - 4

SP - 593

EP - 604

AB - 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.

LA - eng

KW - 31B05

UR - http://eudml.org/doc/268723

ER -

## References

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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] Zbl0473.31007
- [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.

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