Representation of mean-periodic functions in series of exponential polynomials
Let \(\theta\) be a Young function and consider the space \(\mathcal{F}_{\theta}(\C)\) of all entire functions with \(\theta\)-exponential growth. In this paper, we are interested in the solutions \(f\in \mathcal{F}_{\theta}(\C)\) of the convolution equation \(T\star f=0\), called mean-periodic func...
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| description | Let \(\theta\) be a Young function and consider the space \(\mathcal{F}_{\theta}(\C)\) of all entire functions with \(\theta\)-exponential growth. In this paper, we are interested in the solutions \(f\in \mathcal{F}_{\theta}(\C)\) of the convolution equation \(T\star f=0\), called mean-periodic functions, where \(T\) is in the topological dual of \(\mathcal{F}_{\theta}(\C)\). We show that each mean-periodic function can be represented in an explicit way as a convergent series of exponential polynomials. |
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| subjects | Convolution Entire functions Mathematical analysis Periodic functions Polynomials |
| title | Representation of mean-periodic functions in series of exponential polynomials |
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