The Online Books Page

Functional analysis

See also what's at Wikipedia, your library, or elsewhere.

• Calculus of variations

• Integral equations
• Functional equations

• Approximation theory
• Function spaces
• Functor theory
• Operator theory
• Perturbation (Mathematics)
• Spectral theory (Mathematics)
• Topological algebras
• Vector spaces
• Vector valued functions

• Functional calculus

• Actual Causality (Cambridge, MA and London: MIT Press, c2016), by Joseph Y. Halpern (HTML at Cornell)
• Functional Analysis and Semi-Groups (New York: American Mathematical Society, 1948), by Einar Hille (multiple formats at archive.org)

• The Design of Approximation Algorithms (electronic prepublication edition, c2011), by David P. Williamson and David Bernard Shmoys (PDF files with commentary at designofapproxalgs.com)
• The Theory of Approximation (American Mathematical Society Colloquium Publications v11; 1930), by Dunham Jackson (page images at HathiTrust)

• Extrapolation, Interpolation, and Smoothing of Stationary Time Series, With Engineering Applications (second printing; Cambridge, MA: Technology Press of the Massachusetts Institute of Technology; London: J. Wiley and Sons, 1950), by Norbert Wiener (page images at HathiTrust)

• Calculations of the Penetration of Gamma Rays: Final Report (White Plains, NY: Nuclear Development Associates; Oak Ridge, TN: U.S. Atomic Energy Commission, 1954), by Herbert Goldstein and J. Ernest Wilkins (page images at HathiTrust)

• Transition Curves of 330 Mev Bremsstrahlung (Berkeley, CA: University of California Radiation Laboratory, 1950), by Wade Blocker, Robert W. Kenney, and Wolfgang K. H. Panofsky (page images at HathiTrust)

• A Course in Interpolation and Numerical Integration for the Mathematical Laboratory, by David Gibb (page images at Cornell)
• Extrapolation, Interpolation, and Smoothing of Stationary Time Series, With Engineering Applications (second printing; Cambridge, MA: Technology Press of the Massachusetts Institute of Technology; London: J. Wiley and Sons, 1950), by Norbert Wiener (page images at HathiTrust)

• A Course in Interpolation and Numerical Integration for the Mathematical Laboratory, by David Gibb (page images at Cornell)

• Homogeneous Boltzmann Equation in Quantum Relativistic Kinetic Theory (EJDE monograph #4, 2003), by Miguel Escobedo, Stéphane Mischler, and Manuel A. Valle (PDF with commentary at ams.org)

• Rings of Continuous Functions (Princeton, NJ et al.: Van Nostrand, 1960), by Leonard Gillman and Meyer Jerison (page images at HathiTrust)

• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)

• Holomorphic Spaces (1998), ed. by Sheldon Jay Axler, John E. McCarthy, and Donald Sarason (PDF files with commentary at msri.org)

• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem (1984), by Peter B. Gilkey (Postscript files at emis.de)

• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem (1984), by Peter B. Gilkey (Postscript files at emis.de)

• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)

• Spinors, Spectral Geometry, and Riemannian Submersions, by Peter B. Gilkey, John V. Leahy, and Jeonghyeong Park (Postscript files at emis.de)

• Linearization via the Lie Derivative (EJDE monograph #2, 2000), by Carmen Charles Chicone and Richard Swanson (PDF with commentary at ams.org)
• Elementary Divisors and Some Properties of the Lyapunov Mapping X to AX + XA* (Argonne, IL: Argonne National Laboratory, 1961), by Wallace Givens (page images at HathiTrust)

• Jacobi Operators and Completely Integrable Nonlinear Lattices, by Gerald Teschl (PDF and other formats in Austria)

• Operator Algebras and Quantum Statistical Mechanics, by Ola Bratteli and Derek W. Robinson
  • volume I: PDF in Norway
  • volume II: PDF in Norway

• Noncommutative Geometry, Quantum Fields and Motives (prepublication version, ca. 2008), by Alain Connes and Matilde Marcolli (PDF at alainconnes.org)
• Lectures on Graded Differential Algebras and Noncommutative Geometry, by Michel DuBois-Violette (PDF and other formats at arxiv.org)

• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)
• Chebyshev and Fourier Spectral Methods (second edition), by John P. Boyd (PDF with commentary at Citeseer)

• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)

• Harmonic Analysis and the Theory of Probability (Berkeley and Los Angeles: University of California Press, 1955), by S. Bochner (page images at HathiTrust)
• Mathematical Dissertations, For the Use of Students in the Modern Analysis, by J. R. Young (page images at Cornell)
• A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of The Principal Transcendental Functions (second edition; Cambridge, UK: At the University Press, 1915), by E. T. Whittaker and G. N. Watson (multiple formats at archive.org)

• A Presentation of the Theory of Hermite's Form of Lamé's Equation, by J. Brace Chittenden (page images at Cornell)

• An Elementary Treatise on Spherical Harmonics and Subjects Connected With Them, by N. M. Ferrers (page images at Cornell)

• Grassmann's Space Analysis, by E. W. Hyde (page images at Cornell)

• Vector Calculus (electronic edition, 2013 or later), by Michael Corral (PDF with commentary at mecmath.net)

Items below (if any) are from related and broader terms.

• The Logarithmic Potential: Discontinuous Dirichlet and Neumann Problems (American Mathematical Society Colloquium Publications v6; 1927), by Griffith Conrad Evans (page images at HathiTrust)

• Fundamentals of the Laplace Transformation (New York et al.: McGraw-Hill Book Co., c1962), by C. J. Savant, contrib. by Ezra C. Levy (page images at HathiTrust)

• Introduction to Nonlinear Differential and Integral Equations (New York: Dover Publications, 1962), by Harold T. Davis (page images at HathiTrust)

• Functional Differential Geometry (Cambridge, MA and London: MIT Press, c2013), by Gerald Jay Sussman and Jack Wisdom, contrib. by Will Farr (at mitpress.mit.edu PDF with commentary at MIT Press and Dropbox)

• Lecture Notes on Optimization (electronic edition of "Notes on Optimization", 1998), by Pravin Pratap Varaiya (PDF at Berkeley)

• Variational Analysis (based on the third printing of 2009), by R. Tyrrell Rockafellar and Roger J.-B. Wets (PDF at Washington)
• Calculus of Variations (Carus Mathematical Monograph #1; Chicago: Pub. for the Mathematical Association of America by the Open Court Pub. Co., c1925), by Gilbert Ames Bliss (page images at HathiTrust)
• Lectures on the Calculus of Variations (the Weierstrassian Theory), by Harris Hancock (page images at Cornell)
• A Treatise on the Calculus of Variations, by Lewis Buffett Carll (page images at Cornell)
• A Treatise on the Integral Calculus and Its Applications With Numerous Examples (1889 edition), by I. Todhunter (page images at Cornell)

• Convex Analysis (Princeton: Princeton University Press, c1970), by R. Tyrrell Rockafellar (DjVu at Washington)

• Flavors of Geometry (1997), ed. by Silvio Levy (PDF files with commentary at msri.org)

• The Principle of Least Action (reprinted from The Monist; Chicago: Open Court Pub. Co., 1913), by Philip E. B. Jourdain (page images at HathiTrust)