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Introduction to Harmonic Analysis

About this Title

Ricardo A. Sáenz, Universidad de Colima, Colima, Mexico

Publication: The Student Mathematical Library
Publication Year: 2023; Volume 105
ISBNs: 978-1-4704-7199-6 (print); 978-1-4704-7432-4 (online)
DOI: https://doi.org/10.1090/stml/105

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Chapters

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  • Sheldon Axler, Paul Bourdon, and Wade Ramey, Harmonic function theory, 2nd ed., Graduate Texts in Mathematics, vol. 137, Springer-Verlag, New York, 2001. MR 1805196, DOI 10.1007/978-1-4757-8137-3
  • Sheldon Axler, Linear algebra done right, 3rd ed., Undergraduate Texts in Mathematics, Springer, Cham, 2015. MR 3308468, DOI 10.1007/978-3-319-11080-6
  • St. Banach, Sur le théorème de M. Vitali., Fund. Math. 5 (1924), no. 1924, 130–136.
  • Martin T. Barlow, Diffusions on fractals, Lectures on probability theory and statistics (Saint-Flour, 1995) Lecture Notes in Math., vol. 1690, Springer, Berlin, 1998, pp. 1–121. MR 1668115, DOI 10.1007/BFb0092537
  • S. Bernstein, Sur la convergence absolue des séries trigonométriques, C. R. Acad. Sci., Paris 158 (1914), 1661–1663 (French).
  • David M. Bressoud, A radical approach to real analysis, 2nd ed., Classroom Resource Materials Series, Mathematical Association of America, Washington, DC, 2007. MR 2284828
  • David M. Bressoud, A radical approach to Lebesgue’s theory of integration, MAA Textbooks, Cambridge University Press, Cambridge, 2008. MR 2380238
  • Robert G. Bartle and Donald R. Sherbert, Introduction to real analysis, New York, NY: Wiley, 1992 (English).
  • A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 52553, DOI 10.1007/BF02392130
  • P. du Bois-Reymond, Zusätze zur vorstehenden Abhandlung, Math. Ann. 10 (1876), 431–445 (German).
  • Lawrence C. Evans, Partial differential equations, 2nd ed., Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 2010. MR 2597943, DOI 10.1090/gsm/019
  • P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), no. 1, 335–400 (French). MR 1555035, DOI 10.1007/BF02418579
  • L. Fejér, Sur les fonctions bornées et intégrables, Comptes Rendus Hebdomadaries, Seances de l’Academie de Sciences, Paris 131 (1900), 984–987.
  • Wendell Fleming, Functions of several variables, 2nd ed., Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1977. MR 0422527
  • Gerald B. Folland, Introduction to partial differential equations, 2nd ed., Princeton University Press, Princeton, NJ, 1995. MR 1357411
  • Gerald B. Folland, Real analysis, 2nd ed., Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1999. Modern techniques and their applications; A Wiley-Interscience Publication. MR 1681462
  • Joseph Fourier, Analytical theory of heat, Dover Publications, Inc., New York, 1955. Translated, with notes, by Alexander Freeman. MR 0075136
  • Marc Frantz, A fractal made of golden sets, Math. Mag. 82 (2009), no. 4, 243–254. MR 2571788, DOI 10.4169/193009809X468670
  • Theodore W. Gamelin, Complex analysis, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 2001. MR 1830078, DOI 10.1007/978-0-387-21607-2
  • C. F. Gauss, Allgemeine lehrsätze in beziehung auf die verkehrten verhältnisse des quadrats der entfernung wirkenden anziehungs- und abstossungs- kräfte, Weidmann, 1840.
  • Edward D. Gaughan, Introduction to analysis, 3rd ed., Brooks/Cole Publishing Co., Pacific Grove, CA, 1987. MR 1010646
  • Masayoshi Hata, On the structure of self-similar sets, Japan J. Appl. Math. 2 (1985), no. 2, 381–414. MR 839336, DOI 10.1007/BF03167083
  • Felix Hausdorff, Dimension und äußeres Maß, Math. Ann. 79 (1918), no. 1-2, 157–179 (German). MR 1511917, DOI 10.1007/BF01457179
  • G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), no. 1, 81–116. MR 1555303, DOI 10.1007/BF02547518
  • John E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), no. 5, 713–747. MR 625600, DOI 10.1512/iumj.1981.30.30055
  • T. W. Körner, Fourier analysis, Cambridge University Press, Cambridge, 1988. MR 924154, DOI 10.1017/CBO9781107049949
  • Oliver Dimon Kellogg, Foundations of potential theory, Die Grundlehren der mathematischen Wissenschaften, Band 31, Springer-Verlag, Berlin-New York, 1967. Reprint from the first edition of 1929. MR 0222317
  • Jun Kigami, A harmonic calculus on the Sierpiński spaces, Japan J. Appl. Math. 6 (1989), no. 2, 259–290. MR 1001286, DOI 10.1007/BF03167882
  • Jun Kigami, Harmonic calculus on p.c.f. self-similar sets, Trans. Amer. Math. Soc. 335 (1993), no. 2, 721–755. MR 1076617, DOI 10.1090/S0002-9947-1993-1076617-1
  • Jun Kigami, Effective resistances for harmonic structures on p.c.f. self-similar sets, Math. Proc. Cambridge Philos. Soc. 115 (1994), no. 2, 291–303. MR 1277061, DOI 10.1017/S0305004100072091
  • Jun Kigami, Analysis on fractals, Cambridge Tracts in Mathematics, vol. 143, Cambridge University Press, Cambridge, 2001. MR 1840042, DOI 10.1017/CBO9780511470943
  • H. Lebesgue, Sur l’approximation des fonctions, Bull. Sci. Math., II. Sér. 22 (1898), 278–287 (French).
  • H. Lebesgue, Sur la définition de l’aire d’une surface, C. R. Acad. Sci., Paris 129 (1899), 870–873 (French).
  • H. Lebesgue, Sur quelques surfaces non réglées applicables sur le plan, C. R. Acad. Sci., Paris 128 (1899), 1502–1505 (French).
  • H. Lebesgue, Sur la définition de certaines intégrales de surface, C. R. Acad. Sci., Paris 131 (1901), 867–870 (French).
  • H. Lebesgue, Sur le minimum de certaines intégrales, C. R. Acad. Sci., Paris 131 (1901), 935–937 (French).
  • H. Lebesgue, Sur une généralisation de l’intégrale définie, C. R. Acad. Sci., Paris 132 (1901), 1025–1028 (French).
  • H. Lebesgue, Intégrale, longueur, aire, Annali di Mat. (3) 7 (1902), 231–359 (French).
  • H. Lebesgue, Sur les séries trigonométriques, Ann. Sci. École Norm. Sup. (3) 20 (1903), 453–485 (French). MR 1509032
  • H. Lebesgue, Leçons sur l’intégration et la recherche de fonctions primitives, Paris: Gauthier-Villars. VII u. 136 S. $8^\circ$ (1904), 1904.
  • Henri Lebesgue, Sur l’intégration des fonctions discontinues, Ann. Sci. École Norm. Sup. (3) 27 (1910), 361–450 (French). MR 1509126
  • B. Levi, Sopra l’integrazione delle serie, Ist. Lombardo, Rend., II. Ser. 39 (1906), 775–780 (Italian).
  • J. E. Marsden and M. J. Hoffman, Elementary classical analysis, 2 ed., New York, W. H. Freeman and Company, 1993 (English).
  • H. Minkowski, Geometrie der Zahlen. In 2 Lieferungen. Lfg. 1, Leipzig: B. G. Teubner. 240 S. $8^\circ$. (1896)., 1896.
  • P. A. P. Moran, Additive functions of intervals and Hausdorff measure, Proc. Cambridge Philos. Soc. 42 (1946), 15–23. MR 14397, DOI 10.1017/s0305004100022684
  • Camil Muscalu and Wilhelm Schlag, Classical and multilinear harmonic analysis. Vol. I, Cambridge Studies in Advanced Mathematics, vol. 137, Cambridge University Press, Cambridge, 2013. MR 3052498
  • Edward Nelson, A proof of Liouville’s theorem, Proc. Amer. Math. Soc. 12 (1961), 995. MR 259149, DOI 10.1090/S0002-9939-1961-0259149-4
  • M.-A. Parseval des Chênes, Mémoire sur les séries et sur l’intégration complète d’une équation aux differences partielle linéaires du second ordre, à coefficiens constans, Mémoires présentés à l’Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences mathématiques et physiques. (Savants étrangers.), 1806.
  • M. Plancherel, Contribution à l’étude de la représentation d’une fonction arbitraire par des intégrales définies, Rend. Circ. Mat. Palermo 30 (1910), 289–335.
  • S. D. Poisson, Mémoire sur l’intégration de quelques équations linéaires aux différences partielles, et particulièrement de l’équation générale du mouvement des fluides élastiques, Mémoires Acad. Sci. Inst. France 3 (1820), 121–176.
  • R. Rammal, Spectrum of harmonic excitations on fractals, J. Physique 45 (1984), no. 2, 191–206. MR 737523, DOI 10.1051/jphys:01984004502019100
  • B. Riemann, Grundlagen für eine allgemeine theorie der functionen einer veränderlichen complexen grösse, Ph.D. thesis, Göttingen, 1851.
  • Friedrich Riesz, Untersuchungen über Systeme integrierbarer Funktionen, Math. Ann. 69 (1910), no. 4, 449–497 (German). MR 1511596, DOI 10.1007/BF01457637
  • F. Riesz, Les systèmes d’équations linéaires à une infinite d’inconnues, Paris: Gauthier-Villars, VI + 182 S. $8^\circ$. (Collection Borel.) (1913)., 1913.
  • F. Riesz, Sur l’existence de la dérivée des fonctions monotones et sur quelques problèmes qui s’y rattachent, Acta Litt. Sci. Szeged 5 (1932), 208–221 (French).
  • Ricardo A. Sáenz, Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets, J. Fourier Anal. Appl. 18 (2012), no. 2, 240–265. MR 2898728, DOI 10.1007/s00041-011-9194-1
  • Tadashi Shima, On eigenvalue problems for the random walks on the Sierpiński pre-gaskets, Japan J. Indust. Appl. Math. 8 (1991), no. 1, 127–141. MR 1093832, DOI 10.1007/BF03167188
  • W. Sierpiński, Sur une courbe dont tout point est un point de ramification, C. R. Acad. Sci., Paris 160 (1915), 302–305 (French).
  • Michael Spivak, Calculus on manifolds. A modern approach to classical theorems of advanced calculus, W. A. Benjamin, Inc., New York-Amsterdam, 1965. MR 0209411
  • Elias M. Stein and Rami Shakarchi, Fourier analysis, Princeton Lectures in Analysis, vol. 1, Princeton University Press, Princeton, NJ, 2003. An introduction. MR 1970295
  • Elias M. Stein and Rami Shakarchi, Real analysis, Princeton Lectures in Analysis, vol. 3, Princeton University Press, Princeton, NJ, 2005. Measure theory, integration, and Hilbert spaces. MR 2129625
  • Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
  • Robert S. Strichartz, Differential equations on fractals, Princeton University Press, Princeton, NJ, 2006. A tutorial. MR 2246975
  • Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
  • David C. Ullrich, Complex made simple, Graduate Studies in Mathematics, vol. 97, American Mathematical Society, Providence, RI, 2008. MR 2450873, DOI 10.1090/gsm/097
  • G. Vitali, Sui gruppi di punti e sulle funzioni di variabili reali, Torino Atti 43 (1908), 229–246 (Italian).
  • Masaya Yamaguti, Masayoshi Hata, and Jun Kigami, Mathematics of fractals, Translations of Mathematical Monographs, vol. 167, American Mathematical Society, Providence, RI, 1997. Translated from the 1993 Japanese original by Kiki Hudson. MR 1471705, DOI 10.1090/mmono/167