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Certain results on a class of entire functions represented by Dirichlet series having complex frequencies. (English) Zbl 1336.30004

Summary: Consider \(F\) to be a class of entire functions represented by Dirichlet series with complex frequencies for which \((k!)^{c_1} e^{c_2k|\lambda^k|} |a_k|\) is bounded. A study on certain results has been made for this set that is \(F\) is proved to be an algebra with continuous quasi-inverse, commutative Banach algebra with identity etc. Moreover, the conditions for the elements of \(F\) to possess an inverse, quasi-inverse and the form of spectrum of \(F\) are also established.

MSC:

30B50 Dirichlet series, exponential series and other series in one complex variable
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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