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Generalization of weierstrass canonical integrals

✍ Scribed by Olga Veselovska

Book ID
111487677
Publisher
SP Versita
Year
2004
Tongue
English
Weight
233 KB
Volume
2
Category
Article
ISSN
1895-1074

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✦ Synopsis

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

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The integrability problem consists of finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define Weierstrass integrability and we determi