We revisit Fourier’s approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat properties for countably infinite groups and investigate when they are satisfied. Kazhdan’s property (T) is an obstruction to the weakest property, and our findings leave open the possibility that this might be the only one. On the other hand, many groups with the Haagerup property satisfy the strongest version. We show that this heat property implies that the associated heat problem has a unique solution regardless of the choice of the initial datum.

Heat properties for groups / Bedos, E.; Conti, R.. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - 30:4(2024). [10.1007/s00041-024-10103-0]

Heat properties for groups

Conti R.
2024

Abstract

We revisit Fourier’s approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat properties for countably infinite groups and investigate when they are satisfied. Kazhdan’s property (T) is an obstruction to the weakest property, and our findings leave open the possibility that this might be the only one. On the other hand, many groups with the Haagerup property satisfy the strongest version. We show that this heat property implies that the associated heat problem has a unique solution regardless of the choice of the initial datum.
2024
22D25; 22D55; 43A07; 43A35; 43A50; 46L55; 46L57; Fourier series; Haagerup property; Heat equation; Negative definite functions; Property (T); Reduced twisted group C∗-algebras
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Heat properties for groups / Bedos, E.; Conti, R.. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - 30:4(2024). [10.1007/s00041-024-10103-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1719112
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