The nuclear trace of periodic vector‐valued pseudo‐differential operators with applications to index theory

Autor:	Duván Cardona, Vishvesh Kumar
Rok vydání:	2021
Předmět:	Multiplier (Fourier analysis) Pure mathematics Elliptic operator symbols.namesake Fourier transform Trace (linear algebra) Integrable system General Mathematics symbols Torus Differential operator Symbol (chemistry) Mathematics
Zdroj:	Mathematische Nachrichten. 294:1657-1683
ISSN:	1522-2616 0025-584X
DOI:	10.1002/mana.201900040
Popis:	In this paper we investigate the nuclear trace of vector‐valued Fourier multipliers on the torus and its applications to the index theory of periodic pseudo‐differential operators. First we characterise the nuclearity of pseudo‐differential operators acting on Bochner integrable functions. In this regards, we consider the periodic and the discrete cases. We go on to address the problem of finding sharp sufficient conditions for the nuclearity of vector‐valued Fourier multipliers on the torus. We end our investigation with two index formulae. First, we express the index of a vector‐valued Fourier multiplier in terms of its operator‐valued symbol and then we use this formula for expressing the index of certain elliptic operators belonging to periodic Hormander classes.
Databáze:	OpenAIRE
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