On power series in the differentiation operator
Thomas Boehme (1973)
Studia Mathematica
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Displaying similar documents to “On power series in the operators ”
On power series in the differentiation operator
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This paper is concerned with a second-order functional differential equation of the form 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.
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p-Analytic and p-quasi-analytic vectors
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For every symmetric operator acting in a Hilbert space, we introduce the families of p-analytic and p-quasi-analytic vectors (p>0), indexed by positive numbers. We prove various properties of these families. We make use of these families to show that certain results guaranteeing essential selfadjointness of an operator with sufficiently large sets of quasi-analytic and Stieltjes vectors are optimal.