Abstract
In this chapter, we introduce some of the standard notation and review the basic results of analysis used throughout this book.
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Beckner, W.: Inequalities in Fourier analysis. Ann. Math. 102, 159–182 (1975)
Benedetto, J.J.: Harmonic analysis and applications. In: Studies in Advanced Mathematics. CRC, Boca Raton (1997)
Benedetto, J.J., Czaja, W.: Integration and modern analysis. In: Birkhäuser Advanced Texts: Basel Textbooks. Birkhäuser, Boston (2009)
Bényi, Á., Oh, T.: The Sobolev inequality on the torus revisited. Publ. Math. Debr. 83(3), 359–374 (2013)
Cordero, E., Nicola, F.: Remarks on Fourier multipliers and applications to the wave equation. J. Math. Anal. Appl. 353(2), 583–591 (2009)
Cordero, E., Nicola, F.: Sharp integral bounds for Wigner distributions. Int. Math. Res. Not. 6, 177–1807 (2018)
Folland, G.B.: Harmonic analysis in phase space. In: Annals of Mathematical Studies, vol. 122. Princeton University Press, Princeton (1989)
Folland, G.B.: Real analysis. Modern Techniques and Their Applications, 2nd edn. Wiley, New York (1999)
Grafakos, L.: Classical Fourier Analysis, 2nd edn. Graduate Texts in Mathematics, vol. 249. Springer, New York (2008)
Grafakos, L.: Modern Fourier Analysis, 2nd edn. Graduate Texts in Mathematics, vol. 250. Springer, New York (2009)
Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)
Hörmander, L.: Estimates for translation invariant operators in L p spaces. Acta Math. 104, 93–139 (1960)
Kobayashi, M.: Modulation spaces M p, q for 0 < p, q ≤∞. J. Funct. Spaces Appl. 4(3), 329–341 (2006)
Lieb, E.H.: Integral bounds for radar ambiguity functions and Wigner distributions. J. Math. Phys. 31(3), 594–599 (1990)
Pitt, H.R.: Theorems on Fourier series and power series. Duke Math. J. 3, 747–755 (1937)
Rudin, W.: Functional Analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book, New York (1973)
Triebel, H.: Theory of Function Spaces. Birkhäuser, Basel (1983)
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Bényi, Á., Okoudjou, K.A. (2020). Notions of Real, Functional, and Fourier Analysis. In: Modulation Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-0716-0332-1_1
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DOI: https://doi.org/10.1007/978-1-0716-0332-1_1
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