Abstract
I will describe joint work with the late Bob Warner. We knew that \(H^1(\mathbb {R})\) gave better results for singular integrals than \(L^1(\mathbb {R})\); our question was would the same be true for spectral synthesis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Benedetto, J. J.: Spectral Synthesis, B. G. Teubner Stuttgart, (1975).
Beurling, A.: On the spectral synthesis of bounded functions, Acta Math. 81, 225–238 (1949)
Graham, C. C. and McGehee, O. C.: Essays in Commutative Harmonic Analysis, Grundlehren 238, Springer-Verlag, (1979).
Johnson, R. and Warner, C. R.: \(H^1(\mathbb {R})\) as a convolution algebra, J. Function Spaces, 8 no. 2 , 167-179 (2010).
Johnson, R., and C. R. Warner, A characterization of some sets of spectral synthesis. J. Fourier Anal. Appl. v. 27.
Pollard, H.: The harmonic analysis of bounded functions, Duke Math J., 499-512 (1953)
Reiter, H. and Stegeman, J.: Classical Harmonic Analysis and Locally Compact Groups, Oxford Science Publications, Clarendon Press, (2000)
Rudin, W.: Fourier Analysis on Groups, Interscience Publishers, John Wiley and Sons, Second Printing, (1967)
Stein, E.: Harmonic Analysis, Princeton University Press, Princeton, NJ, (1993)
French lecture notes, Synthese Harmonique, Faculté des Sciences, Nancy, D. E. A. de Mathématiques Pures,1966-67
Acknowledgement
Thanks to Kasso Okoudjou for his help with modern LaTeX.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Johnson, R. (2021). Spectral Synthesis and \(H^1(\mathbb {R})\) . In: Hirn, M., Li, S., Okoudjou, K.A., Saliani, S., Yilmaz, Ö. (eds) Excursions in Harmonic Analysis, Volume 6. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-69637-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-69637-5_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-69636-8
Online ISBN: 978-3-030-69637-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)