Universal Series and Fundamental Solutions of the Cauchy-Riemann Operator

Stefanopoulos, Vangelis

doi:10.1007/bf03321710

Cited by 3 publications

(4 citation statements)

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“…The aim of this paper is to generalize those ideas to the case of non-compact Riemann surfaces. One of the main tools used by Stefanopoulos to prove those theorems was an abstract characterization of universality that we shall now present (see [8,Theorem 2.1], or [4,Proposition 7] along with [7,Theorem 1.2]).…”

Section: Theorem 11 Let K Be a Compact Subset Of C With Connected Comentioning

confidence: 99%

“…The other crucial result in [8] is a theorem on approximation by fundamental solutions of a differential operator, which we recall here in the particular case that is of interest to us (see [9]).…”

Section: Is Dense In X For All N ∈ N;mentioning

confidence: 99%

“…In [8], Stefanopoulos shows the existence of a series of fundamental solutions of the Cauchy-Riemann operator that are universal on subsets of C. More precisely, he obtains the following theorems.…”

Section: Introductionmentioning

confidence: 99%

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Universal Series on a Riemann Surface

Clouâtre¹

2011

Can. j. math.

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Section: Theorem 11 Let K Be a Compact Subset Of C With Connected Comentioning

confidence: 99%

Section: Is Dense In X For All N ∈ N;mentioning

confidence: 99%

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Universal Series on a Riemann Surface

Clouâtre¹

2011

Can. j. math.

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“…Special cases of Theorem 2.7 regarding universal series whose terms are translates of fundamental solutions of elliptic operators, translates of approximate identities or translates of fundamental solutions of the ∂-operator can be found in [11,12,14,16].…”

Section: Examplesmentioning

confidence: 99%

Universal series in ∩_p
>1 ℓ^p

Koumandos¹,

Nestoridis²,

Smyrlis³

et al. 2009

Bulletin of the London Mathematical Society

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In this paper an abstract condition is given yielding universal series defined by sequences a = {a j } ∞ j=1 in ∩p>1 p but not in 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.

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