Abstract
We extend the large sieve type estimates to sums involving \(p\)th powers of trigonometric polynomials. An approach to such estimates that does not rely on the usual \(L^2\)-technique is given. Our method is based on comparing the norm and the spectral radius of convolution operators on a normed space of trigonometric polynomials.
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Norvidas, S. Some inequalities of the large sieve type. Acta Math. Hungar. 166, 205–215 (2022). https://doi.org/10.1007/s10474-022-01211-8
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DOI: https://doi.org/10.1007/s10474-022-01211-8
Key words and phrases
- trigonometric polynomial
- large sieve inequality
- convolution of measures
- linear operator in a normed space
- spectral radius of a linear operator