References
- C.I. Christov, A complete orthonormal system of functions in L2 (−∞, ∞) space, SIAM J. Appl. Math. 42(6) (1982), 1337–1344, DOI 10.1137/0142093.
- M. Cotlar, A combinatorial inequality and its applications to L2 -spaces, Rev. Mat. Cuyana 1 (1955), 41–56.
- J. Duoandikoetxea, Fourier analysis, Graduate Studies in Mathematics, Vol. 29, American Mathematical Society, Providence, RI, 2001.
- J. Duoandikoetxea, The Hilbert transform and Hermite functions: a real variable proof of the L -isometry, J. Math. Anal. Appl. 347(2) (2008), 592–596, DOI 10.1016/j.jmaa.2008.06.016.
- L. Grafakos, Classical Fourier analysis, third ed., Graduate Texts in Mathematics, Vol. 249, Springer, New York, 2014.
- J.R. Higgins, Completeness and basis properties of sets of special functions, Cambridge University Press, London/New York/Melbourne, 1977.
- E. Laeng, A simple real-variable proof that the Hilbert transform is an L2- isometry, C. R. Math. Acad. Sci. Paris, 348(17–18) (2010), 977–980, DOI 10.1016/j.crma.2010.07.002.