Advanced Real Analysis

Transcription

1 Selected References, DOI: /euclid/ from Advanced Real Analysis Digital Second Edition Corrected version 2017 Anthony W. Knapp Full Book DOI: /euclid/ ISBN: Distributed by Project Euclid. For copyright information, see the following page.

2 Anthony W. Knapp 81 Upper Sheep Pasture Road East Setauket, N.Y , U.S.A. to: Homepage: aknapp Title: Advanced Real Analysis Cover: Normal distribution as a limit of Gosset s t distribution; see page 421. Mathematics Subject Classification (2010): 46 01, 42 01, 43 01, 35 01, 34 01, 47 01, 58 01, 60A99, 60F05, 28C10, 42C40, 65T60. First Edition, ISBN c 2007 Anthony W. Knapp Published by Birkhäuser Boston Digital Second Edition, not to be sold, no ISBN c 2016 Anthony W. Knapp, corrected version issued in 2017 Published by the Author All rights reserved. This file is a digital second edition of the above named book. The text, images, and other data contained in this file, which is in portable document format (PDF), are proprietary to the author, and the author retains all rights, including copyright, in them. The use in this file of trade names, trademarks, service marks, and similar items, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. All rights to print media for the first edition of this book have been licensed to Birkhäuser Boston, c/o Springer Science+Business Media Inc., 233 Spring Street, New York, NY 10013, USA, and this organization and its successor licensees may have certain rights concerning print media for the digital second edition. The author has retained all rights worldwide concerning digital media for both the first edition and the digital second edition. The file is made available for limited noncommercial use for purposes of education, scholarship, and research, and for these purposes only, or for fair use as understood in the United States copyright law. Users may freely download this file for their own use and may store it, post it online, and transmit it digitally for purposes of education, scholarship, and research. They may not convert it from PDF to any other format (e.g., EPUB), they may not edit it, and they may not do reverse engineering with it. In transmitting the file to others or posting it online, users must charge no fee, nor may they include the file in any collection of files for which a fee is charged. Any exception to these rules requires written permission from the author. Except as provided by fair use provisions of the United States copyright law, no extracts or quotations from this file may be used that do not consist of whole pages unless permission has been granted by the author (and by Birkhäuser Boston if appropriate). The permission granted for use of the whole file and the prohibition against charging fees extend to any partial file that contains only whole pages from this file, except that the copyright notice on this page must be included in any partial file that does not consist exclusively of the front cover page. Such a partial file shall not be included in any derivative work unless permission has been granted by the author (and by Birkhäuser Boston if appropriate). Inquiries concerning print copies of either edition should be directed to Springer Science+Business Media Inc.

3 SELECTED REFERENCES Adams, M., and V. Guillemin, Measure Theory and Probability, Wadsworth & Brooks/Cole Advanced Books and Software, Monterey, CA 1986; corrected reprint of the original, Birkhäuser Boston, Inc., Boston, Ahlfors, L. V., Lectures on Quasiconformal Mappings, D. Van Nostrand Company, Inc., Toronto, 1966; reprinted, Wadsworth Brooks/Cole Advanced Books and Software, Monterey, CA, Austin, D., Image compression: seeing what s not there, feature column, American Mathematical Society, September 2007, samplings/feature-column/fcarc-image-compression. Austin, D., What is JPEG?, Notices of the American Mathematical Society 55 (2008), Bailey, B. A., Lecture Notes on Multivariate Statistics, Summer 2009, downloaded from babailey/reut09. Lectures 9 and 11 (Chapter 6) are relevant to the present Chapter IX. Bers, L., F. John, and M. Schechter, Partial Differential Equations, Interscience Publishers, Inc., New York, 1964; reprinted, American Mathematical Society, Providence, Brislawn, C. M., Fingerprints go digital, Notices of the American Mathematical Society 42 (1995), Burris, C. S., R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms, a Primer, Prentice-Hall, Upper Saddle River, NJ, Cartan, É., Sur la détermination d un système orthogonal complet dans un espace de Riemann symétrique clos, Rend. Circ. Mat. Palermo 53 (1929), Chui, C. K., An Introduction to Wavelets, Academic Press, Inc., Boston, Churchill, R. V., Fourier Series and Boundary Value Problems, McGraw Hill Book Company, New York, 1941; second edition Coddington, E. A., and N. Levinson, Theory of Ordinary Differential Equations, McGraw Hill Book Company, New York, Courant, R., and D. Hilbert, Methods of Mathematical Physics, John Wiley & Sons, New York. Vol. I, 1953, reprinted, 1989; Vol. II, Partial Differential Equations, 1962, reprinted, Daubechies, I., Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, Debnath, L., Wavelet Transforms and Their Applications, Birkhäuser Boston, Inc., Boston,

4 604 Selected References Doob, J. L., Measure Theory, Springer-Verlag, New York, Duistermaat, J. J., and J. A. C. Kolk, Multidimensional Real Analysis, Cambridge University Press, Cambridge, Vol. I, Differentiation; Vol. II, Integration. Dunford, N., and J. T. Schwartz, Linear Operators, Interscience Publishers, Inc., New York, Part 1, General Theory, 1958; Part 2, Spectral Theory, 1963; Part 3 Spectral Operators, Elkies, N.D., One of the answers to a question about central binomial coefficients, Feller, W., An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley & Sons, New York, 1966; second edition, Friedman, A., Partial Differential Equations, Holt, Rinehart and Winston, New York, Gelfand, I. M., and G. E. Shilov, Generalized Functions, Academic Press, New York. Vol. 1, Properties and Operations, 1964; Vol. 2, Spaces of Fundamental and Generalized Functions, 1968; Vol. 3, Theory of Differential Equations, All reprinted, Gelfand, I. M., and N. Ya. Vilenkin, Generalized Functions, Academic Press, New York. Vol. 4, Applications of Harmonic Analysis, Reprinted, Gelfand, I. M., M. I. Graev, and N. Ya. Vilenkin, Generalized Functions, Academic Press, New York. Vol. 5, Integral Geometry and Representation Theory, Reprinted, Halmos, P. R., Introduction to Hilbert Space, Chelsea Publishing Company, New York, 1951; second edition, Halmos, P. R., Measure Theory, D. Van Nostrand Company, Inc., Princeton, 1950; reprinted, Springer-Verlag, New York, Hernandez, E., and G. Weiss, A First Course on Wavelets, CRC Press, Inc., Boca Raton, FL, Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall, Inc., Englewood Cliffs, NJ, Hörmander, L., The Analysis of Linear Partial Differential Operators, Springer- Verlag, Berlin. Vol. I, Distribution Theory and Fourier Analysis, 1983; Vol. II, Differential Operators with Constant Coefficients, 1983; Vol. III, Pseudodifferential Operators, 1985; Vol. IV, Fourier Integral Operators, Hubbard, B. B., The World According to Wavelets, A.K. Peters, Ltd., Wellesley, MA, 1996; second Edition Ince, E. L., Ordinary Differential Equations, Longmans, Green and Co., London, 1927; reprinted, Dover Publications, New York, Kelley, J. L., General Topology, D. Van Nostrand Company, Inc., Princeton, 1955; reprinted, Springer-Verlag, New York, Kelley, J. L., I. Namioka, et al., Linear Topological Spaces, D. Van Nostrand Company, Inc., Princeton, Knapp, A. W., Elliptic Curves, Princeton University Press, Princeton, 1992.

5 Selected References 605 Knapp, A. W., Basic Real Analysis, Birkhäuser, Boston, 2005; digital second edition, Knapp, A. W., Basic Algebra, Birkhäuser, Boston, 2006; digital second edition, Kolmogorov, A. N., Foundations of the Theory of Probability, Chelsea Publishing Company, 1950; second English edition, Original German edition published Lawson, H. B., and M.-L. Michelsohn, Spin Geometry, Princeton University Press, Princeton, Lax, P. D., Partial Differential Equations, Notes by J. Berkowitz and A. and P. Lax, , New York University, Courant Institute of Mathematical Sciences. Lebanon, G., The Analysis of Data Project, downloaded as of January 2015 from The project advertises itself as featuring comprehensive coverage of all relevant disciplines including probability, statistics, computing, and machine learning. Chapter 8 of Volume I is relevant to the present Chapter IX. Lewy, H., An example of a smooth linear partial differential equation without solution, Annals of Math. 66 (1957), Liouville, J., Sur le développement des fonctions ou parties de fonctions en séries dont les divers termes sont assujettis à satisfaire à une même équation différentielle du second ordre contenant un paramètre variable II, Journal de Mathématiques Pures et Appliquées 2 (1837), Loomis, L. H., An Introduction to Abstract Harmonic Analysis, D. Van Nostrand Company, Inc., New York, Louis, A. K., P. Maass, and A. Rieder, Wavelets, Theory and Applications, Pure and Applied Mathematics, John Wiley and Sons, Chichester, Meyer, Y., Wavelets and Operators, Cambridge University Press, Cambridge, Munroe, M. E., Introduction to Measure and Integration, Addison Wesley Publishing Company, Inc., Cambridge, MA, 1953; second edition, Measure and Integration, Addison Wesley Publishing Company, Reading, MA, Naimark, M. A., Normed Rings, P. Noordhoff, Groningen, Netherlands, Pierce, L. B., Hardy Functions, Junior Paper written under the direction of E. M. Stein, Princeton University, Princeton, May 2001, downloaded as of July 2016 from lbpierce/theses/ Pierce Junior Paper.pdf. Pinsky, M. A., Introduction to Fourier Analysis and Wavelets, American Mathematical Society, Providence, RI, Rabbani, M., and R. Joshi, An overview of the JPEG 2000 still image compression standard, Signal Processing: Image Communication 17 (2002), Riesz, F., and B. Sz.-Nagy, Functional Analysis, Frederick Ungar Publishing Co., New York, Royden, H. L., Real Analysis, The Macmillan Company, New York, 1963; second edition, Macmillan Publishing Co., 1968, third edition, 1988.

6 606 Selected References Rudin, W., Real & Complex Analysis, McGraw Hill Book Company, New York, 1966; second edition 1974, third edition Saks, S., Theory of the Integral, second revised edition, G. E. Stechart and Company, New York, 1937; reprinted, Hafner Publishing Company, New York, no date, and Dover Publications, New York, Schwartz, L., Théorie des Distributions, Hermann, Paris, Sokolnikoff, I. S., and R. M. Redheffer, Mathematics of Physics and Modern Engineering, McGraw Hill Book Company, New York, 1958; second edition Spivak, M., Calculus on Manifolds, Benjamin/Cummings Publishing Company, Menlo Park, CA, Steenrod, N., The Topology of Fibre Bundles, Princeton University Press, Princeton, 1951; reprinted, Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, Stein, E. M., and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, Stein, E. M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, Sturm, C., Sur les équations différentielles linéaires du second ordre, Journal de Mathématiques Pures et Appliquées 1 (1836), Taylor, M. E., Pseudodifferential Operators, Princeton University Press, Princeton, Treves, F., Basic Linear Partial Differential Equations, Academic Press, Orlando, Treves, F., Introduction to Pseudodifferential and Fourier Integral Operators, Plenum Press, New York, Vol. 1, Pseudodifferential Operators; Vol. 2, Fourier Integral Operators. Treves, F., Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, Wallace, G. K., The JPEG still picture compression standard, IEEE Transactions on Consumer Electronics 38 (1992), xviii xxxiv. Weil, A., L intégration dans les Groupes Topologiques et Ses Applications, Actualités Scientifiques et Industrielles, vol. 869, Hermann, Paris, 1940; second edition, vol. 1145, Wells, R. O., Differential Analysis on Complex Manifolds, Prentice Hall, Inc., Englewood Cliffs, NJ, 1973; second edition, Springer-Verlag, New York, 1980.