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PreprintCC BY 4.0HAL

PSEUDOSPECTRAL PHENOMENA PREVENTING THE ANALYTICITY SECTOR OF A ORNSTEIN-UHLENBECK SEMIGROUP TO BE RULED BY THE SPECTRAL ANGLE OF ITS GENERATOR

  • Karel Pravda-Starov
Open at sourcePDFDOICite

Abstract

We study elliptic Ornstein-Uhlenbeck operators in L2 spaces with respect to invariant measures. These operators have discrete spectra and generate analytic semigroups. The angle defining the analyticity sector of a Ornstein-Uhlenbeck semigroup is not always equal to the complementary angle of the spectral angle of its generator. In this work, we study the link between these two angles. More specifically, we provide a necessary and sufficient criterion ensuring that they are complementary, and explain how pseudospectral phenomena account for these two angles to fail to be complementary.

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Cite

BibTeXRIS
BibTeX
@misc{pravdastarov2026pseudospectral,
  title = {{PSEUDOSPECTRAL PHENOMENA PREVENTING THE ANALYTICITY SECTOR OF A ORNSTEIN-UHLENBECK SEMIGROUP TO BE RULED BY THE SPECTRAL ANGLE OF ITS GENERATOR}},
  author = {Karel Pravda-Starov},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33683},
  eprint = {2610.33683},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05838453v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - PSEUDOSPECTRAL PHENOMENA PREVENTING THE ANALYTICITY SECTOR OF A ORNSTEIN-UHLENBECK SEMIGROUP TO BE RULED BY THE SPECTRAL ANGLE OF ITS GENERATOR
AU  - Karel Pravda-Starov
PY  - 2026
DA  - 2026/10/24
PB  - HAL
DO  - 10.48550/arxiv.2610.33683
UR  - https://hal.science/hal-05838453v1
AB  - We study elliptic Ornstein-Uhlenbeck operators in L^2 spaces with respect to invariant measures. These operators have discrete spectra and generate analytic semigroups. The angle defining the analyticity sector of a Ornstein-Uhlenbeck semigroup is not always equal to the complementary angle of the spectral angle of its generator. In this work, we study the link between these two angles. More specifically, we provide a necessary and sufficient criterion ensuring that they are complementary, and explain how pseudospectral phenomena account for these two angles to fail to be complementary.
ER  -