Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake

Sabrina Kombrink; Lucas Schmidt

doi:10.48550/arXiv.2312.12331

Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake

Sabrina Kombrink, Lucas Schmidt

Mathematics

Research output: Working paper/Preprint › Preprint

Abstract

We apply recent results by the authors to obtain bounds on remainder terms of the Dirichlet Laplace eigenvalue counting function for domains that can be realised as countable disjoint unions of scaled Koch snowflakes. Moreover we compare the resulting exponents to the exponents in the asymptotic expansion of the domain's inner parallel volume.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2312.12331
Publication status	Published - 19 Dec 2023

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Added details, fixed typos. 15 pages, 10 figures.

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10.48550/arXiv.2312.12331Licence: Creative Commons: Attribution-NonCommercial-ShareAlike (CC BY-NC-SA)

2312.12331v2Other version, 1.7 MBLicence: Creative Commons: Attribution-NonCommercial-ShareAlike (CC BY-NC-SA)

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abstract = "We apply recent results by the authors to obtain bounds on remainder terms of the Dirichlet Laplace eigenvalue counting function for domains that can be realised as countable disjoint unions of scaled Koch snowflakes. Moreover we compare the resulting exponents to the exponents in the asymptotic expansion of the domain's inner parallel volume.",

author = "Sabrina Kombrink and Lucas Schmidt",

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Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake

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