SPECTRAL MULTIPLIER THEOREMS FOR ABSTRACT DIFFERENTIAL OPERATORS

DOI10.1017/s0004972723000369OpenAlexW4382560507WikidataQ122940876 ScholiaQ122940876MaRDI QIDQ6082068

Himani Sharma

Publication date: 3 November 2023

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972723000369

zbMATH Keywords

harmonic oscillatorscanonical commutation relationstransferencesquare functionsRiesz transformSobolev embeddingtwisted convolutionsspectral multiplier theoremsPhillips functional calculusHörmander functional calculusWeyl pseudo-differential calculus

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Multipliers for harmonic analysis in several variables (42B15) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Functional calculus for linear operators (47A60) Groups and semigroups of linear operators (47D03) General theory of partial differential operators (47F05) Multipliers in one variable harmonic analysis (42A45) Pseudodifferential operators (47G30)

Cites Work

• Bounds on the Phillips calculus of abstract first order differential operators
• Vertical and horizontal square functions on a class of non-doubling manifolds
• Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices

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