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PreprintCC BY 4.0arXiv

An interpolation problem for extended Gevrey regularity

  • Jelena Dimitrić
  • Đorđe Vučković
  • Milica Žigić
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Abstract

We study an interpolation problem in extended Gevrey classes defined by the sequences Mnτ,σ=nτnσ, n∈ℕ, τ>0, σ>1. We show that, under a suitable growth condition on a divergent sequence of derivative orders, estimates of extended Gevrey type imposed only along this sequence imply corresponding estimates for all derivative orders. In particular, we explicitly quantify the change of the parameters in the resulting estimates. To this end, we first establish an equivalence between two definitions of the extended Gevrey classes, one involving the supergeometric factor hnσ and another in which this factor is omitted. We then establish a corresponding interpolation principle for extended Gelfand--Shilov spaces, including a symmetric characterization and a formulation in terms of the associated function of the defining sequence.

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Cite

BibTeXRIS
BibTeX
@misc{dimitric2026interpolation,
  title = {{An interpolation problem for extended Gevrey regularity}},
  author = {Jelena Dimitrić and Đorđe Vučković and Milica Žigić},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06258},
  eprint = {2609.06258},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06258},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An interpolation problem for extended Gevrey regularity
AU  - Jelena Dimitrić
AU  - Đorđe Vučković
AU  - Milica Žigić
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.06258
UR  - https://arxiv.org/abs/2609.06258
AB  - We study an interpolation problem in extended Gevrey classes defined by the sequences M_n^τ,σ=n^τn^σ, n∈ℕ, τ>0, σ>1. We show that, under a suitable growth condition on a divergent sequence of derivative orders, estimates of extended Gevrey type imposed only along this sequence imply corresponding estimates for all derivative orders. In particular, we explicitly quantify the change of the parameters in the resulting estimates. To this end, we first establish an equivalence between two definitions of the extended Gevrey classes, one involving the supergeometric factor h^n^σ and another in which this factor is omitted. We then establish a corresponding interpolation principle for extended Gelfand--Shilov spaces, including a symmetric characterization and a formulation in terms of the associated function of the defining sequence.
ER  -