Corpus ID: 235694532

On the Fourier coefficients of powers of a Blaschke factor and strongly annular fonctions

@inproceedings{Borichev2021OnTF,
  title={On the Fourier coefficients of powers of a Blaschke factor and strongly annular fonctions},
  author={A. Borichev and K. Fouchet and R. Zarouf},
  year={2021}
}
We compute asymptotic formulas for the k Fourier coefficients of bλ, where bλ(z) = z−λ 1−λz is the Blaschke factor associated to λ ∈ D, k ∈ [0,∞) and n is a large integer. We distinguish several regions of different asymptotic behavior of those coefficients in terms of k and n. Given β ∈ ((1−λ)/(1+λ), (1+λ)/(1−λ)) their decay is oscillatory for k ∈ [βn, n/β]. Given α ∈ (0, (1− λ)/(1 + λ)) their decay is exponential for k ∈ [0, nα] ∪ [n/α,∞).Airy-type behavior is happening near the k-transition… Expand

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