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This is a section of the Basic Math Library List


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 8. Analysis
    Classical analysis. Special functions. Harmonic analysis. Complex analysis in one and several variables,
    potential theory, geometric function theory (including quasi-conformal mappings),
    geometric measure theory. Applications. 
    Connections with sections 5, 6, 7, 9, 10, 11, 12, 16.




Folland, Gerald B.(1-WA) Real analysis. Modern techniques and their applications. Second edition. Pure and Applied Mathematics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999. xvi+386 pp. \$74.95. ISBN 0-471-31716-0

Rudin, Walter(1-WI) Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. xiv+416 pp. \$44.95. ISBN 0-07-054234-1

Jost, Jürgen(D-MPI-NS) Postmodern analysis. Second edition. Universitext. Springer-Verlag, Berlin, 2003. xviii+367 pp. \$44.95. ISBN 3-540-43873-4

Folland, Gerald B.(1-WA) A course in abstract harmonic analysis. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995. x+276 pp. \$61.95. ISBN 0-8493-8490-7

Folland, Gerald B.(1-WA) Fourier analysis and its applications. The Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1992. x+433 pp. \$59.50. ISBN 0-534-17094-3

Stein, Elias M.; Weiss, Guido Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, No. 32. Princeton University Press, Princeton, N.J., 1971. x+297 pp. \$15.00.

Stein, Elias M.(1-PRIN); Shakarchi, Rami(1-PRIN) Fourier analysis. An introduction. Princeton Lectures in Analysis, 1. Princeton University Press, Princeton, NJ, 2003. xvi+311 pp. \$49.95. ISBN 0-691-11384-X


Foundations of Analysis

Barnier, William and Feldman, Norman. Introduction to Advanced Mathematics Englewood Cliffs, NJ: Prentice Hall, 1990.

Bittinger, Marvin L. Logic, Proof, and Sets, Reading, MA: Addison-Wesley, 1982. Second Edition.

Feferman, Solomon. The Number Systems: Foundations of Algebra and Analysis, New York, NY: Chelsea, 1989. Second Edition.

  • Fendel, Daniel and Resek, Diane. Foundations of Higher Mathematics: Exploration and Proof Reading, MA: Addison-Wesley, 1990.
  • Gardiner, A. Infinite Processes: Background to Analysis New York, NY: Springer-Verlag, 1982.

Gleason, Andrew M. Fundamentals of Abstract Analysis Boston, MA: Jones and Bartlett, 1991.

    • Landau, Edmund G.H. The Foundations of Analysis, New York, NY: Chelsea, 1951, 1966. Third Edition.

Lightstone, A.H. Symbolic Logic and the Real Number System: An Introduction to the Foundations of Number Systems New York, NY: Harper and Row, 1965.

Lucas, John F. Introduction to Abstract Mathematics, New York, NY: Ardsley House, 1990. Second Edition.

Smith, D.; Eggen, M.; and St.~Andre, R. A Transition to Advanced Mathematics, Pacific Grove, CA: Brooks/Cole, 1990. Third Edition.

    • Solow, Daniel. How To Read and Do Proofs: An Introduction to Mathematical Thought Processes, New York, NY: John Wiley, 1982, 1990. Second Edition.

Elementary Real Analysis

Aliprantis, Charalambos D. and Burkinshaw, Owen. Principles of Real Analysis New York, NY: Elsevier Science, 1981.

  • Apostol, Tom M. Mathematical Analysis, Reading, MA: Addison-Wesley, 1974. Second Edition.
  • Bartle, Robert G. Elements of Real Analysis, New York, NY: John Wiley, 1976. Second Edition.

Binmore, K.G. Mathematical Analysis: A Straightforward Approach, New York, NY: Cambridge University Press, 1977, 1981. 2 Vols.

Burkill, John C. A First Course in Mathematical Analysis New York, NY: Cambridge University Press, 1978.

Goffman, Casper. Real Functions, Boston, MA: Prindle, Weber and Schmidt, 1967. Revised Edition.

  • Goldberg, Richard R. Methods of Real Analysis, New York, NY: John Wiley, 1976. Second Edition.

Kolmogorov, Andrei N. and Fomin, S.V. Introductory Real Analysis Mineola, NY: Dover, 1975.

Protter, Murray H. and Morrey, C.B. A First Course in Real Analysis New York, NY: Springer-Verlag, 1977.

Rosenlicht, Maxwell. Introduction to Analysis Mineola, NY: Dover, 1986.

    • Ross, Kenneth A. Elementary Analysis: The Theory of Calculus New York, NY: Springer-Verlag, 1980.
    • Royden, H.L. Real Analysis, New York, NY: Macmillan, 1968, 1988. Third Edition.
      • Rudin, Walter. Principles of Mathematical Analysis, New York, NY: McGraw-Hill, 1953, 1976. Third Edition.

Smith, Kennan T. Primer of Modern Analysis New York, NY: Springer-Verlag, 1983.

Wheeden, Richard L. and Zygmund, Antoni. Measure and Integral: An Introduction to Real Analysis New York, NY: Marcel Dekker, 1977. Analysis: Advanced Real Analysis Akhiezer, N.I. The Classical Moment Problem New York, NY: Hafner Press, 1965.

Beals, R. Advanced Mathematical Analysis New York, NY: Springer-Verlag, 1973.

  • Bishop, Errett and Bridges, Douglas S. Constructive Analysis New York, NY: Springer-Verlag, 1985.
      • Boas, Ralph P., Jr. A Primer of Real Functions, Washington, DC: Mathematical Association of America, 1972, 1981. Third Edition.

Burkill, John C. The Lebesgue Integral New York, NY: Cambridge University Press, 1951.

Caratheodory, C. Algebraic Theory of Measure and Integration, New York, NY: Chelsea, 1986. Second English Edition.

Fischer, Emanuel. Intermediate Real Analysis New York, NY: Springer-Verlag, 1983.

      • Gelbaum, Bernard R. and Olmsted, John M.H. Theorems and Counterexamples in Mathematics New York, NY: Springer-Verlag, 1990. (Former title: Counterexamples in Analysis.)
      • Gillman, Leonard and Jerison, Meyer. Rings of Continuous Functions New York, NY: Springer-Verlag, 1976.

Grenander, Ulf and Szeg o, Gabor. Toeplitz Forms and Their Applications New York, NY: Chelsea, 1984.

    • Halmos, Paul R. Measure Theory New York, NY: Springer-Verlag, 1974.

Hardy, G.H. Divergent Series New York, NY: Oxford University Press, 1949.

  • Hewitt, Edwin and Stromberg, Karl R. Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable New York, NY: Springer-Verlag, 1969, 1975.

Karlin, Samuel and Studden, W. Tchebycheff Systems New York, NY: John Wiley, 1966.

Moise, Edwin E. Introductory Problem Courses in Analysis and Topology New York, NY: Springer-Verlag, 1982.

Munkres, James R. Analysis on Manifolds Reading, MA: Addison-Wesley, 1991.

Munroe, Marshall E. Introduction to Measure and Integration, Reading, MA: Addison-Wesley, 1971. Second Edition.

      • Polya, George and Szeg o, Gabor. Problems and Theorems in Analysis, New York, NY: Springer-Verlag, 1972, 1976. 2 Vols.

Stromberg, Karl R. Introduction to Classical Real Analysis Belmont, CA: Wadsworth, 1981.

Taylor, Angus E. General Theory of Functions and Integration Mineola, NY: Dover, 1985.

  • Wagon, Stan. The Banach-Tarski Paradox New York, NY: Cambridge University Press, 1985.


Measure Theory

Ash, Robert B. Real Analysis and Probability New York, NY: Academic Press, 1972.

Bauer, Heinz. Probability Theory and Elements of Measure Theory, New York, NY: Academic Press, 1978, 1981. Second English Edition.

  • Billingsley, Patrick. Convergence of Probability Measures New York, NY: John Wiley, 1968.
    • Billingsley, Patrick. Probability and Measure, New York, NY: John Wiley, 1979, 1986. Second Edition.

Dudley, Richard M. Real Analysis and Probability Belmont, CA: Wadsworth, 1989.

Kallenberg, Olav. Random Measures New York, NY: Academic Press, 1983.

  • Kingman, J.F.C. and Taylor, S.J. Introduction to Measure with Probability New York, NY: Cambridge University Press, 1966.
  • Krieger, Henry A. Measure-theoretic Probability Lanham, MD: University Press of America, 1980.
    • Parthasarathy, K.R. Probability Measures on Metric Spaces New York, NY: Academic Press, 1967.

Fourier Analysis

Chandrasekharan, Komaravolu. Classical Fourier Transforms New York, NY: Springer-Verlag, 1989.

Chihara, T.S. An Introduction to Orthogonal Polynomials New York, NY: Gordon and Breach, 1978.

Davies, B. Integral Transforms and their Applications, New York, NY: Springer-Verlag, 1978, 1985. Second Edition.

  • Dym, H. and McKean, H. Fourier Series and Integrals New York, NY: Academic Press, 1972.

Edwards, Robert E. Fourier Series: A Modern Introduction, New York, NY: Springer-Verlag, 1979, 1982. 2 Vols., Second Edition.

Jackson, Dunham. Fourier Series and Orthogonal Polynomials Washington, DC: Mathematical Association of America, 1941.

  • Korner, T.W. Fourier Analysis New York, NY: Cambridge University Press, 1988.

Rogosinski, Werner. Fourier Series, New York, NY: Chelsea, 1962. Second Edition.

Seeley, Robert T. An Introduction to Fourier Series and Integrals Reading, MA: W.A. Benjamin, 1966.

++** Stein, E.M. and Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces Princeton, NJ: Princeton University Press, 1971.

  • Szeg o, Gabor. Orthogonal Polynomials, Providence, RI: American Mathematical Society, 1975. Fourth Edition.
  • Titchmarsh, Edward C. Introduction to the Theory of Fourier Integrals London: Oxford University Press, 1948.

Widder, David V. An Introduction to Transform Theory New York, NY: Academic Press, 1971.

    • Wiener, Norbert. The Fourier Integral and Certain of its Applications New York, NY: Cambridge University Press, 1933, 1988.
      • Zygmund, Antoni. Trigonometric Series New York, NY: Cambridge University Press, 1968, 1988.

Introductory Complex Analysis

+*** Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, New York, NY: McGraw-Hill, 1966, 1979. Third Edition.

Bak, Joseph and Newman, Donald J. Complex Analysis New York, NY: Springer-Verlag, 1982.

  • Boas, Ralph P., Jr. Invitation to Complex Analysis New York, NY: Birkhauser, 1987.

Burckel, Robert B. An Introduction to Classical Complex Analysis New York, NY: Academic Press, 1979.

Cartan, Henri. Theory of Analytic Functions of One or Several Complex Variables Reading, MA: Addison-Wesley, 1983.

+** Conway, John B. Functions of One Complex Variable, New York, NY: Springer-Verlag, 1973, 1978. Second Edition.

Heins, Maurice. Complex Function Theory New York, NY: Academic Press, 1968.

  • Knopp, Konrad. Theory of Functions, Mineola, NY: Dover, 1945, 1947; 1968. 2 Vols.

Markushevich, A.I. The Theory of Analytic Functions: A Brief Course Moscow: MIR, 1983.

Narasimhan, R. Complex Analysis in One Variable New York, NY: Birkhauser, 1985.

Nehari, Zeev. Introduction to Complex Analysis, Boston, MA: Allyn and Bacon, 1968. Revised Edition.

Nevanlinna, Rolf and Paatero, V. Introduction to Complex Analysis Reading, MA: Addison-Wesley, 1969.

  • Polya, George and Latta, Gordon. Complex Variables New York, NY: John Wiley, 1974.

Analysis: Advanced Complex Analysis

  • Caratheodory, C. Theory of Functions of a Complex Variable, New York, NY: Chelsea, 1958. 2 Vols.

Davis, Philip J. The Schwarz Function and Its Applications Washington, DC: Mathematical Association of America, 1974.

Fisher, Stephen D. Complex Variables, Belmont, CA: Wadsworth, 1986, 1990. Second Edition.

Grauert, H. and Fritzsche, K. Several Complex Variables New York, NY: Springer-Verlag, 1976.

    • Henrici, Peter. Applied and Computational Complex Analysis, New York, NY: John Wiley, 1974--86. 3 Vols.
  • Hille, Einar. Analytic Function Theory, New York, NY: Chelsea, 1973. 2 Vols.

Jones, William B. and Thron, Wolfgang J. Continued Fractions: Analytic Theory and Applications Reading, MA: Addison-Wesley, 1980.

      • Krantz, Steven G. Complex Analysis: The Geometric Viewpoint Washington, DC: Mathematical Association of America, 1990.
  • Littlewood, J.E. Some Problems in Real and Complex Analysis Lexington, MA: D.C. Heath, 1968.
  • Nehari, Zeev. Conformal Mapping Mineola, NY: Dover, 1979.

Price, G. Baley. An Introduction to Multicomplex Spaces and Functions New York, NY: Marcel Dekker, 1991.

  • Remmert, Reinhold. Theory of Complex Functions New York, NY: Springer-Verlag, 1991.
      • Rudin, Walter. Real and Complex Analysis, New York, NY: McGraw-Hill, 1974, 1987. Third Edition.
    • Saks, S. and Zygmund, Antoni. Analytic Functions, New York, NY: American Elsevier, 1952, 1971. Third Edition.

Smith, Kennan T. Power Series from a Computational Point of View New York, NY: Springer-Verlag, 1987.

  • Springer, George M. Introduction to Riemann Surfaces Reading, MA: Addison-Wesley, 1957.
    • Titchmarsh, Edward C. Theory of Functions, New York, NY: Oxford University Press, 1939. Second Edition.

Wermer, John. Banach Algebras and Several Complex Variables, New York, NY: Springer-Verlag, 1976. Second Edition.

  • Weyl, Hermann. The Concept of a Riemann Surface Reading, MA: Addison-Wesley, 1964.
      • Whittaker, Edmund T. and Watson, G.N. A Course of Modern Analysis, New York, NY: Cambridge University Press, 1958, 1963. Fourth Edition.


Inequalities

    • Beckenbach, Edwin F. and Bellman, Richard E. An Introduction to Inequalities Washington, DC: Mathematical Association of America, 1975.

Beckenbach, Edwin F. and Bellman, Richard E. Inequalities, New York, NY: Springer-Verlag, 1961, 1965. Second Edition.

      • Hardy, G.H.; Littlewood, J.E.; and Polya, George. Inequalities, New York, NY: Cambridge University Press, 1952, 1988. Second Edition.
  • Kazarinoff, Nicholas D. Analytic Inequalities New York, NY: Holt, Rinehart and Winston, 1961.

Korovkin, P.P. Inequalities Moscow: MIR, 1975, 1986.

Marshall, Albert W. and Olkin, Ingram. Inequalities: Theory of Majorization and Its Applications New York, NY: Academic Press, 1979.

Tong, Y. L. Probability Inequalities in Multivariate Distributions New York, NY: Academic Press, 1980.

Harmonic Analysis

    • Ash, J.M., ed. Studies in Harmonic Analysis Washington, DC: Mathematical Association of America, 1976.

Helson, Henry. Harmonic Analysis Belmont, CA: Wadsworth, 1991.

  • Katznelson, Yitzhak. An Introduction to Harmonic Analysis, Mineola, NY: Dover, 1976. Second Edition.

Loomis, Lynn H. An Introduction to Abstract Harmonic Analysis New York, NY: Van Nostrand Reinhold, 1953.

  • Rudin, Walter. Fourier Analysis on Groups New York, NY: John Wiley, 1990.

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