204

Bibliography

[Abb] S. Abbott, Understanding analysis, Undergraduate Texts in Mathematics, Springer, 2001.

[Ari] J. Arias de Reyna, Pointwise convergence of Fourier series, Lecture Notes in Math., vol. 1785, Springer–Verlag, Berlin, 2002.

[Bart1] R. G. Bartle, The elements of integration and Lebesgue measure, John Wiley & Sons, Inc., 1966.

[Bart2] R. G. Bartle, A modern theory of integration, Graduate Studies in Mathematics, vol. 32, Amer. Math. Soc., Providence, RI, 2001.

[Bre] D. M. Bressoud, A radical approach to real analysis, Math. Assoc. of Amer., Washington, DC, 1994.

[Cal] A. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190.

[Car] L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157.

[CM] R. R. Coifman and Y. Meyer, Remarques sur l’analyse de Fourier à fenêtre, C. R. Acad. Sci. Paris, Série I 312 (1991), 259–261.

[CW] R. R. Coifman and V. Wickerhauser, Entropy-based algorithms for best basis selection, IEEE Trans. Information Theory 38 (1992), 713–718.

[CT] J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 (1965), 297–301.

[Dau92] I. Daubechies, Ten lectures on wavelets, CBMS–NSF Lecture Notes, vol. 61, SIAM, Philadelphia, PA, 1992.

[Dau98] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure and Appl. Math. 41 (1998), 909–996.

[Duo] J. Duoandikoetxea, Fourier analysis, English transl. by D. Cruz-Uribe, SFO, Graduate Studies in Mathematics, vol. 29, Amer. Math. Soc., Providence, RI, 2001.

[DM] H. Dym and H. P. McKean, Fourier series and integrals, Probability and Mathematical Statistics, vol. 14, Academic Press, New York–London, 1972.

[Fol] G. B. Folland, Real analysis: Modern techniques and their applications, Wiley, New York, NY, 1999.

[Fra] M. W. Frazier, An introduction to wavelets through linear algebra, Springer–Verlag, New York, NY, 1999.

[Gab] D. Gabor, Theory of communication, J. Inst. Electr. Eng., London 93 (III) (1946), 429– 457.

[Grab] J. V. Grabiner, Who gave you the epsilon? Cauchy and the origins of rigorous calculus, Amer. Math. Monthly 90 No. 3 (1983), 185–194.

[Graf] L. Grafakos, Classical and modern Fourier analysis, Prentice Hall, 2004.

[Grat] I. Grattan-Guinness, The development of the foundations of mathematical analysis from Euler to Riemann, MIT Press, Cambridge, MA, 1970.

[Haa] A. Haar, Zur Theorie der orthogonalen Funktionensysteme, Math. Annal. 69 (1910), 331–371.

[HW] E. Hernandez and G. Weiss, A first course on wavelets, CRC Press, Boca Raton, FL, 1996.

[Hun] R. Hunt, On the convergence of Fourier series, Orthogonal expansions and their continuous analogues (Proc. Conf., Edwardsville, IL, 1967), Southern Illinois Univ. Press, Carbondale, IL, 1968, pp. 235–255.

[JMR] S. Jaffard, Y. Meyer, and R.D. Ryan, Wavelets: Tools for science and technology, revised edition, SIAM, Philadelphia, PA, 2001.

[KK] J.-P. Kahane and Y. Katznelson, Sur les ensembles de divergence des séries trigonométriques, Studia Math. 26 (1966), 305–306.

[KL] J.-P. Kahane and P.-G. Lemarié-Rieusset, Fourier series and wavelets, Gordon and Breach Publishers, 1995.

[Kat] Y. Katznelson, Introduction to harmonic analysis, Dover Publications Inc., 1976.

[Kol] A. Kolmogorov, Une série de Fourier–Lebesgue divergente partout, C. R. Acad. Sci. Paris 183 (1926), 1327–1328.

[Kor] T. W. Körner, Fourier analysis, Cambridge Univ. Press, Cambridge, 1988.

[Kra] S. G. Krantz, A panorama of harmonic analysis, The Carus Mathematical Monographs, vol. 27, Amer. Math. Soc., Providence, RI, 1999.

[Mall89] S. Mallat, Multiresolution approximations and wavelet orthonormal bases for L^{2}(ℝ), Trans. Amer. Math. Soc. 315 (1989), 69–87.

[Mall98] S. Mallat, A wavelet tour of signal processing, Academic Press, San Diego, CA, 1998.

[Malv] H. Malvar, Lapped transforms for efficient transform/subband coding, IEEE Trans. Acoust. Speech Signal Process 38 (1990), 969–978.

[Pin] M. A. Pinsky, Introduction to Fourier analysis and wavelets, The Brooks/Cole Series in Advanced Mathematics (Paul J. Sally, Jr, ed.), Brooks/Cole, 2001.

[RS] M. Reed and B. Simon, Methods of modern mathematical physics, Vol. II: Fourier analysis, self-adjointness, Academic Press, 1975.

[Roy] H. L. Royden, Real analysis, 2nd ed., MacMillan, New York, NY, 1968.

[Rud] W. Rudin, Principles of mathematical analysis, McGraw–Hill, New York, NY, 1976.

[Sch] M. Schechter, Principles of functional analysis, Graduate Studies in Mathematics, vol. 36, 2nd ed., Amer. Math. Soc., Providence, RI, 2002.

[Sha] C. E. Shannon, Communications in the presence of noise, Proc. Inst. Radio Eng. 37 (1949), 10–21.

[Spi] M. Spiegel, Schaum’s outline of Fourier analysis with applications to boundary value problems, McGraw–Hill, New York, NY, 1974.

[SS1] E. Stein and R. Shakarchi, Fourier analysis: an introduction, Princeton Lectures in Analysis I, Princeton Univ. Press, Princeton, NJ, 2003.

[SS2] E. Stein and R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton Lectures in Analysis III, Princeton Univ. Press, Princeton, NJ, 2005.

[SW] E. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, NJ, 1971.

[SN] G. Strang and T. Nguyen, Wavelets and filter banks, Wellesley–Cambridge Press, Wellesley, MA, 1996.

[Str] R. S. Strichartz, The way of analysis, Jones & Bartlett Publishers; revised edition, 2000.

[Str2] R. S. Strichartz, A guide to distribution theory and Fourier transforms, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1994.

[Tao1] T. Tao, Analysis I, Text and Readings in Mathematics, vol. 37, Hindustan Book Agency, India, 2006.

[Tao2] T. Tao, Analysis II, Text and Readings in Mathematics, vol. 37, Hindustan Book Agency, India, 2006.

[Ter] A. Terras, Fourier analysis on finite groups and applications, London Math. Soc. Student Texts, vol. 43, Cambridge Univ. Press, Cambridge, 1999.

[VK] M. Vetterli and J. Kovačević, Wavelets and subband coding, Prentice Hall, Upper Saddle River, NJ, 1995.

[Wic] V. Wickerhauser, Adapted wavelet analysis from theory to software, A. K. Peters, Wellesley, 1994.