Riesz and Green energy on projective spaces

Austin Anderson; Daria Dostert; Peter Grabner; Ryan William Matzke; Tetiana Stepaniuk

doi:10.1090/btran/161

Riesz and Green energy on projective spaces

Austin Anderson, Daria Dostert, Peter Grabner^*, Ryan William Matzke, Tetiana Stepaniuk

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude.

Original language	English
Pages (from-to)	1039-1076
Journal	Transactions of the American Mathematical Society
Volume	10
DOIs	https://doi.org/10.1090/btran/161
Publication status	Published - 26 Jul 2023

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https://arxiv.org/abs/2204.04015Licence: CC BY 4.0

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title = "Riesz and Green energy on projective spaces",

abstract = "In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude. ",

author = "Austin Anderson and Daria Dostert and Peter Grabner and Matzke, {Ryan William} and Tetiana Stepaniuk",

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AU - Anderson, Austin

AU - Dostert, Daria

AU - Grabner, Peter

AU - Matzke, Ryan William

AU - Stepaniuk, Tetiana

PY - 2023/7/26

Y1 - 2023/7/26

N2 - In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude.

AB - In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude.

U2 - 10.1090/btran/161

DO - 10.1090/btran/161

M3 - Article

SN - 0002-9947

VL - 10

SP - 1039

EP - 1076

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Riesz and Green energy on projective spaces

Abstract

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