Displaying similar documents to “A class of gap theorems”

Analytic solutions of a second-order functional differential equation with a state derivative dependent delay

Jian-Guo Si, Xin-Ping Wang (1999)

Colloquium Mathematicae

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This paper is concerned with a second-order functional differential equation of the form x ' ' ( z ) = x ( a z + b x ' ( z ) ) with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

Analytic continuation of Dirichlet series.

J. Milne Anderson, Dimitry Khavinson, Harold S. Shapiro (1995)

Revista Matemática Iberoamericana

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The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series Σ a ζ (where 0 < |a| < 1) is nowhere continuable across {|ζ| = 1}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial...