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Ingham Inequality
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(Theorem)
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Let $(t_{j})_{j \in \mathbb{Z}}$ a increasing sequence of positive real numbers such that $$ t_{j + 1} - t_{j} \geq \gamma > 1, \quad j \in \mathbb{Z}. $$ Then for all $n \in \mathbb{N}$ and for all complex sequences $(c_{j})_{j = -n}^{n}$ we have $$ m \sum_{j = -n}^{n} |c_{j}|^{2} \leq \int_{-\pi}^{\pi} \left| \sum_{j = -n}^{n} \sqrt{\frac{1}{2\pi}} c_{j}e^{i t_{j} x} \right|^{2} dx, $$ where
$$ m = \frac{2}{\pi}\left( 1 - \frac{1}{\gamma^{2}} \right). $$
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"Ingham Inequality" is owned by ncrom.
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Cross-references: complex, real numbers, positive, sequence, increasing
This is version 5 of Ingham Inequality, born on 2006-05-19, modified 2006-06-12.
Object id is 7920, canonical name is InghamInequality.
Accessed 1224 times total.
Classification:
| AMS MSC: | 42B05 (Fourier analysis :: Fourier analysis in several variables :: Fourier series and coefficients) |
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Pending Errata and Addenda
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