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A study of various results for a class of entire Dirichlet series with complex frequencies

Niraj Kumar, Garima Manocha (2018)

Mathematica Bohemica

Let F be a class of entire functions represented by Dirichlet series with complex frequencies a k e λ k , z for which ( | λ k | / e ) | λ k | k ! | a k | is bounded. Then F is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. F is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to F have also been established.

An analogue of Montel’s theorem for some classes of rational functions

R. K. Kovacheva, Julian Lawrynowicz (2002)

Czechoslovak Mathematical Journal

For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best L p -approximation with an unbounded number of finite poles are considered.

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