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Universal series in ∩ p >1 ℓ p
Author(s) -
Koumandos S.,
Nestoridis V.,
Smyrlis Y.S.,
Stefanopoulos V.
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp102
Subject(s) - mathematics , series (stratigraphy) , operator (biology) , constant (computer programming) , pure mathematics , riemann hypothesis , dirichlet series , function (biology) , identity (music) , combinatorics , dirichlet distribution , mathematical analysis , boundary value problem , paleontology , biochemistry , chemistry , physics , repressor , evolutionary biology , biology , computer science , transcription factor , acoustics , gene , programming language
In this paper an abstract condition is given yielding universal series defined by sequences a ={ a j }j = 1 ∞in ∩ p >1 ℓ p but not in ℓ 1 . We obtain a unification of some known results related to approximation by translates of specific functions including the Riemann ζ‐function, or a fundamental solution of a given elliptic operator in ℝ ν with constant coefficients or an approximate identity as, for example, the normal distribution. Another application gives universal trigonometric series in ℝ ν simultaneously with respect to all σ‐finite Borel measures in ℝ ν . Stronger results are obtained by using universal Dirichlet series.