Skip to Main Content


AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution


Functional Analysis: An Elementary Introduction

About this Title

Markus Haase, Delft University of Technology, Delft, The Netherlands

Publication: Graduate Studies in Mathematics
Publication Year: 2014; Volume 156
ISBNs: 978-0-8218-9171-1 (print); 978-1-4704-1858-8 (online)
DOI: https://doi.org/10.1090/gsm/156
MathSciNet review: MR3237610
MSC: Primary 46-01

PDF View full volume as PDF

Read more about this volume

View other years and volumes:

Table of Contents

PDF Download chapters as PDF

Front/Back Matter

Chapters

References [Enhancements On Off] (What's this?)

References
  • Robert G. Bartle, The Elements of Integration and Lebesgue Measure, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1995.
  • —, A Modern Theory of Integration, Graduate Studies in Mathematics, vol. 32, American Mathematical Society, Providence, RI, 2001.
  • Heinz Bauer, Measure and Integration Theory, de Gruyter Studies in Mathematics, vol. 26, Walter de Gruyter & Co., Berlin, 2001, Translated from the German by Robert B. Burckel.
  • Kurt Bryan and Tanya Leise, The $\$25,000,000,000$ eigenvector: the linear algebra behind Google, SIAM Rev. 48 (2006), no. 3, 569–581 (electronic).
  • Ralph P. Boas, A Primer of Real Functions, fourth ed., Carus Mathematical Monographs, vol. 13, Mathematical Association of America, Washington, DC, 1996, Revised and with a preface by Harold P. Boas.
  • Adam Bobrowski, Functional Analysis for Probability and Stochastic Processes, Cambridge University Press, Cambridge, 2005.
  • Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157.
  • Paul R. Chernoff, Pointwise convergence of Fourier series, Amer. Math. Monthly 87 (1980), no. 5, 399–400.
  • Ward Cheney, Analysis for Applied Mathematics, Graduate Texts in Mathematics, vol. 208, Springer-Verlag, New York, 2001.
  • James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414.
  • John B. Conway, A Course in Functional Analysis, second ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990.
  • —, A Course in Operator Theory, Graduate Studies in Mathematics, vol. 21, American Mathematical Society, Providence, RI, 2000.
  • Jean Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1969, Enlarged and corrected printing, Pure and Applied Mathematics, Vol. 10-I.
  • —, History of Functional Analysis, North-Holland Mathematics Studies, vol. 49, North-Holland Publishing Co., Amsterdam, 1981, Notas de Matemática [Mathematical Notes], 77.
  • Ben de Pagter and Arnoud C.M. van Rooij, An Invitation to Functional Analysis, Epsilon Uitgaven, vol. 75, CWI Amsterdam, 2013.
  • Klaus-Jochen Engel and Rainer Nagel, A Short Course on Operator Semigroups, Universitext, Springer, New York, 2006.
  • Per Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309–317.
  • Lawrence C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 1998.
  • Israel Gohberg, Seymour Goldberg, and Marinus A. Kaashoek, Basic Classes of Linear Operators, Birkhäuser Verlag, Basel, 2003.
  • Sudhir R. Ghorpade and Balmohan V. Limaye, A Course in Calculus and Real Analysis, Undergraduate Texts in Mathematics, Springer, New York, 2006.
  • Markus Haase, The Functional Calculus for Sectorial Operators, Operator Theory: Advances and Applications, vol. 169, Birkhäuser Verlag, Basel, 2006.
  • —, Convexity inequalities for positive operators, Positivity 11 (2007), no. 1, 57–68.
  • Paul R. Halmos, What does the spectral theorem say?, Amer. Math. Monthly 70 (1963), 241–247.
  • Shizuo Kakutani, Weak topology and regularity of Banach spaces, Proc. Imp. Acad., Tokyo 15 (1939), 169–173.
  • Yitzhak Katznelson, An Introduction to Harmonic Analysis, third ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2004.
  • Thomas W. Körner, Fourier Analysis, second ed., Cambridge University Press, Cambridge, 1989.
  • Serge Lang, Real and Functional Analysis, third ed., Graduate Texts in Mathematics, vol. 142, Springer-Verlag, New York, 1993.
  • Peter D. Lax, Functional Analysis, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002.
  • Peter D. Lax and Arthur N. Milgram, Parabolic equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N. J., 1954, pp. 167–190.
  • Amy N. Langville and Carl D. Meyer, Google’s PageRank and Beyond: the Science of Search Engine Rankings, Princeton University Press, Princeton, NJ, 2006.
  • Antonie Frans Monna, Functional Analysis in Historical Perspective, John Wiley & Sons, New York-Toronto, Ont., 1973.
  • Joachim Naumann, Remarks on the prehistory of Sobolev spaces, Unpublished Preprint, 2002.
  • Albrecht Pietsch, History of Banach Spaces and Linear Operators, Birkhäuser Boston, Inc., Boston, MA, 2007.
  • Allan Pinkus, Weierstrass and approximation theory, J. Approx. Theory 107 (2000), no. 1, 1–66.
  • Inder K. Rana, An Introduction to Measure and Integration, second ed., Graduate Studies in Mathematics, vol. 45, American Mathematical Society, Providence, RI, 2002.
  • Frigyes Riesz, Sur les opérations fonctionnelles linéaires., C. R. Acad. Sci., Paris 149 (1910), 974–977 (French).
  • Walter Rudin, Real and Complex Analysis, third ed., McGraw-Hill Book Co., New York, 1987.
  • —, Functional Analysis, second ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991.
  • René L. Schilling, Measures, Integrals and Martingales, Cambridge University Press, New York, 2005.
  • Ralph E. Showalter, Hilbert Space Methods for Partial Differential Equations, Pitman, London, 1977, Monographs and Studies in Mathematics, Vol. 1.
  • Alan D. Sokal, A really simple elementary proof of the uniform boundedness theorem, Amer. Math. Monthly 118 (2011), 450–452.
  • Reinhard Siegmund-Schultze, The origins of functional analysis, A History of Analysis, Hist. Math., vol. 24, Amer. Math. Soc., Providence, RI, 2003, pp. 385–407.
  • Elias M. Stein and Rami Shakarchi, Fourier Analysis, Princeton Lectures in Analysis, vol. 1, Princeton University Press, Princeton, NJ, 2003.
  • Lynn A. Steen, Highlights in the history of spectral theory, Amer. Math. Monthly 80 (1973), 359–381.
  • Karl Weierstrass, Über die analytische Darstellbarkeit sogenannter willkürlicher Functionen einer reellen Veränderlichen. (On the analytic representability of so called arbitrary functions of a real variable.), Sitzungsberichte der Akademie zu Berlin (1885), 633–639 and 789–806 (German).
  • Dirk Werner, Funktionalanalysis, extended ed., Springer-Verlag, Berlin, 2000.
  • Hermann Weyl, The method of orthogonal projection in potential theory, Duke Math. J. 7 (1940), 411–444.
  • Nicholas Young, An Introduction to Hilbert Space, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1988.
  • Eberhard Zeidler, Applied Functional Analysis, Applied Mathematical Sciences, vol. 109, Springer-Verlag, New York, 1995, Main principles and their applications.
  • —, Applied Functional Analysis, Applied Mathematical Sciences, vol. 108, Springer-Verlag, New York, 1995, Applications to mathematical physics.