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PreprintCC BY 4.0arXiv

Eberlein convolution as an inner product and quantitative Bombieri--Taylor results

  • Daniel Lenz
  • Nicolae Strungaru
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Abstract

We present a simple argument providing a very general Bombieri--Taylor-type result to compute Bragg peaks in diffraction theory as limits. At its abstract core the argument relies on considering the Eberlein convolution as an inner product. This inner product gives an abstract version of a Cauchy--Schwarz type inequality which implies the Bombieri--Taylor-type result as well as generalizations.

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Cite

BibTeXRIS
BibTeX
@misc{lenz2026eberlein,
  title = {{Eberlein convolution as an inner product and quantitative Bombieri--Taylor results}},
  author = {Daniel Lenz and Nicolae Strungaru},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19501},
  eprint = {2609.19501},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19501},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Eberlein convolution as an inner product and quantitative Bombieri--Taylor results
AU  - Daniel Lenz
AU  - Nicolae Strungaru
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19501
UR  - https://arxiv.org/abs/2609.19501
AB  - We present a simple argument providing a very general Bombieri--Taylor-type result to compute Bragg peaks in diffraction theory as limits. At its abstract core the argument relies on considering the Eberlein convolution as an inner product. This inner product gives an abstract version of a Cauchy--Schwarz type inequality which implies the Bombieri--Taylor-type result as well as generalizations.
ER  -