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THE RESOLVENT AND RIESZ TRANSFORM ON CONNECTED SUMS OF MANIFOLDS WITH DIFFERENT ASYMPTOTIC DIMENSIONS

Part of: Special classes of linear operators General theory of linear operators Infinite-dimensional manifolds

Published online by Cambridge University Press:  24 June 2021

DANIEL NIX
DANIEL NIX*
Affiliation:
Mathematical Sciences Institute, The Australian National University, Canberra, ACT 2601, Australia
*
e-mail: daniel.nix@anu.edu.au
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Abstract

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Keywords

analysis on manifoldslow energy resolventRiesz transform

MSC classification

Primary: 58B20: Riemannian, Finsler and other geometric structures
Secondary: 47A10: Spectrum, resolvent 47B06: Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

Information

Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 344 - 345
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to the Australian National University in December 2019; degree approved on 29 September 2020; supervisors Andrew Hassell and Adam Sikora.

References

Hassell, A. and Sikora, A., ‘Riesz transforms in one dimension’, Indiana Univ. Math. J. 58(2) (2009), 823–852.CrossRefGoogle Scholar
Hassell, A. and Sikora, A., ‘Riesz transforms on a class of non-doubling manifolds’, Comm. Partial Differential Equations 44(11) (2019), 1072–1099.CrossRefGoogle Scholar