Fourier Analysis
Körner, “Fourier analysis”
Stein, Shakarchi, “Fourier Analysis”
Folland, “Real Analysis: Modern Techniques and Their Applications”
Folland, “Introduction to Partial Differential Equations”
Dym, McKean, “Fourier Series and Integrals”
Tolstov, “Fourier Series”
Google / fourier transform / discrete fourier transform / distribution fourier transform / laplace transform / filter convolution / linear differential equation
Brown, Churchill, “Fourier Series and Boundary Value Problems”
G. Folland, “Tata notes on PDE”
Rudin, “Functional Analysis”
Paul Garrett, “Functions on circles”
R.Bhatia, “Fourier series”
D.M.Bressoud, “A radical approach to Lebesgue theory of Integration”
http://www.cargalmathbooks.com/#FourierAnalysis
Bracewell, Ronald. The Fourier Transform and Its Applications, 2nd ed. McGraw-Hill. 1986.
Papoulis, Athanasios. The Fourier Integral and Its Applications. McGraw-Hill. 1962.
Folland, Gerald B. Fourier Analysis and its Applications. Wadsworth and Brooks/Cole. 1992. 0534170943
Morrison, Norman. Introduction to Fourier Analysis. Wiley. 1994. 047101737X
Solymar, L. Lectures on Fourier Series. Oxford. 1988. 0198561997
Pinkus, Allan, and Samy Zafrany. Fourier Series and Integral Transforms. Cambridge. 1997. 0521597714
James, J. F. A Student’s Guide to Fourier Transforms with Applications in physics and Engineering. Cambridge. 1995. 052180826X
The Fourier Transform in Biomedical Engineering
Fourier Transform for Finance
Meikle, “A New Twist to Fourier Transforms”
Bracewell’s book
Erwin Kreyszig, “Advanced Engineering Mathematics”
Sneddon, “Fourier Transforms”
Taub and Schilling, “Principles of Communication Systems”
Jack D. Gaskill, “Linear Systems, Fourier Transforms, and Optics”
David W. Kammler, “A First Course in Fourier Analysis”
“Fourier Transform in one day” http://www.dspdimension.com/admin/dft-a-pied/
J. S. Walker, “Fourier Analysis”
J. M. Ash (ed.), “Studies in Harmonic Analysis”
S. G. Krantz, “A Panorama of Harmonic Analysis”
A. Zygmund, “Trigonometric Series”
G. H. Hardy and W. W. Rogosinski, “Fourier Series”
W. L. Briggs and V. E. Henson, “The DFT: An Owner’s Manual for the Discrete Fourier Transform”
A. Terras, “Fourier Analysis on Finite Groups and Applications”
R. Strichartz, “A Guide to Distributions and Fourier Transforms” by
Tables of Fourier Transforms
Erdelyi, “Tables of Integral Transforms”
Gradshteyn and Ryzhik, “Table of Integrals, Series, and Products”
D. Van Nostrand, “Fourier Integrals for Practical Applications”
R. M. Gray and J. W. Goodman, “Fourier Transforms”
S. Papoulis, “The Fourier Transform and its Applications”
S. Papoulis, “Systems and Transforms With Applications in Optics”
S. Papoulis, “Probability, Random Variables, and Stochastic Processes”
P. J. Nahim, “The Science of Radio”
E. O. Brigham, “The Fast Fourier Transform”
C van Loam, “Computational Frameworks for the Fast Fourier Transform”
A. Terras, “Harmonic Analysis on Symmetric Spaces and Applications”
• Offner, “A Little Harmonic Analysis”
•
o Y. Katznelson
o Helgason
• Error-correcting codes
o van Lint “Coding Theory”
• Orthogonal polynomials
o Davis “Interpolation and Approximation”
o Szegö “Orthogonal polynomials”
Click to access 01fourier-1.pdf
Askey, R. and Haimo, D. T. “Similarities between Fourier and Power Series.” Amer. Math. Monthly 103, 297-304, 1996.
Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, 1987.
Byerly, W. E. An Elementary Treatise on Fourier’s Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, 1959.
Carslaw, H. S. Introduction to the Theory of Fourier’s Series and Integrals, 3rd ed., rev. and enl. New York: Dover, 1950.
Davis, H. F. Fourier Series and Orthogonal Functions. New York: Dover, 1963.
Groemer, H. Geometric Applications of Fourier Series and Spherical Harmonics. New York: Cambridge University Press, 1996.
Krantz, S. G. “Fourier Series.” §15.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 195-202, 1999.
Lighthill, M. J. Introduction to Fourier Analysis and Generalised Functions. Cambridge, England: Cambridge University Press, 1958.
Morrison, N. Introduction to Fourier Analysis. New York: Wiley, 1994.
Sansone, G. “Expansions in Fourier Series.” Ch. 2 in Orthogonal Functions, rev. English ed. New York: Dover, pp. 39-168, 1991.
Weisstein, E. W. “Books about Fourier Transforms.” http://www.ericweisstein.com/encyclopedias/books/FourierTransforms.html.
Whittaker, E. T. and Robinson, G. “Practical Fourier Analysis.” Ch. 10 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 260-284, 1967.
From Fourier Analysis to Wavelets
作者：Jonas Gomes，Luiz Velho
Fourier Analysis and Approximation
Graduate level
• Grafakos, “Classical and Modern Fourier Analysis”
• Sogge, “Fourier Integrals in Classical Analysis”
distribution theory, and theory of partial/pseudo/para-differential operators
• Friendlander and Joschi, “Introduction to the theory of distributions”
• Hörmander, “Analysis of Linear Partial Differential Operators”
• Alinhac and Gérard, “Pseudo-differential Operators and the Nash-Moser Theorem”
Fourier Analysis
Körner, “Fourier analysis”
Stein, Shakarchi, “Fourier Analysis”
Folland, “Real Analysis: Modern Techniques and Their Applications”
Folland, “Introduction to Partial Differential Equations”
Dym, McKean, “Fourier Series and Integrals”
Tolstov, “Fourier Series”
Google / fourier transform / discrete fourier transform / distribution fourier transform / laplace transform / filter convolution / linear differential equation
Brown, Churchill, “Fourier Series and Boundary Value Problems”
G. Folland, “Tata notes on PDE”
Rudin, “Functional Analysis”
Paul Garrett, “Functions on circles”
R.Bhatia, “Fourier series”
D.M.Bressoud, “A radical approach to Lebesgue theory of Integration”
Bracewell, Ronald. The Fourier Transform and Its Applications, 2nd ed. McGraw-Hill. 1986.
Papoulis, Athanasios. The Fourier Integral and Its Applications. McGraw-Hill. 1962.
Folland, Gerald B. Fourier Analysis and its Applications. Wadsworth and Brooks/Cole. 1992.0534170943
Morrison, Norman. Introduction to Fourier Analysis. Wiley. 1994. 047101737X
Solymar, L. Lectures on Fourier Series. Oxford. 1988.0198561997
Pinkus, Allan, and Samy Zafrany. Fourier Series and Integral Transforms. Cambridge. 1997.0521597714
James, J. F. A Student’s Guide to Fourier Transforms with Applications in physics and Engineering. Cambridge. 1995. 052180826X
The Fourier Transform in Biomedical Engineering
Fourier Transform for Finance
Meikle, “A New Twist to Fourier Transforms”
Bracewell’s book
Erwin Kreyszig, “Advanced Engineering Mathematics”
Sneddon, “Fourier Transforms”
Taub and Schilling, “Principles of Communication Systems”
Jack D. Gaskill, “Linear Systems, Fourier Transforms, and Optics”
David W. Kammler, “A First Course in Fourier Analysis”
“Fourier Transform in one day” http://www.dspdimension.com/admin/dft-a-pied/
J. S. Walker, “Fourier Analysis”
J. M. Ash (ed.), “Studies in Harmonic Analysis”
S. G. Krantz, “A Panorama of Harmonic Analysis”
A. Zygmund, “Trigonometric Series”
G. H. Hardy and W. W. Rogosinski, “Fourier Series”
W. L. Briggs and V. E. Henson, “The DFT: An Owner’s Manual for the Discrete Fourier Transform”
A. Terras, “Fourier Analysis on Finite Groups and Applications”
R. Strichartz, “A Guide to Distributions and Fourier Transforms” by
Tables of Fourier Transforms
Erdelyi, “Tables of Integral Transforms”
Gradshteyn and Ryzhik, “Table of Integrals, Series, and Products”
D. Van Nostrand, “Fourier Integrals for Practical Applications”
R. M. Gray and J. W. Goodman, “Fourier Transforms”
S. Papoulis, “The Fourier Transform and its Applications”
S. Papoulis, “Systems and Transforms With Applications in Optics”
S. Papoulis, “Probability, Random Variables, and Stochastic Processes”
P. J. Nahim, “The Science of Radio”
E. O. Brigham, “The Fast Fourier Transform”
C van Loam, “Computational Frameworks for the Fast Fourier Transform”
A. Terras, “Harmonic Analysis on Symmetric Spaces and Applications”
• Offner, “A Little Harmonic Analysis”
•
o Y. Katznelson
o Helgason
• Error-correcting codes
o van Lint “Coding Theory”
• Orthogonal polynomials
o Davis “Interpolation and Approximation”
o Szegö “Orthogonal polynomials”
Askey, R. and Haimo, D. T. “Similarities between Fourier and Power Series.” Amer. Math. Monthly 103, 297-304, 1996.
Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, 1987.
Byerly, W. E. An Elementary Treatise on Fourier’s Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, 1959.
Carslaw, H. S. Introduction to the Theory of Fourier’s Series and Integrals, 3rd ed., rev. and enl. New York: Dover, 1950.
Davis, H. F. Fourier Series and Orthogonal Functions. New York: Dover, 1963.
Groemer, H. Geometric Applications of Fourier Series and Spherical Harmonics. New York: Cambridge University Press, 1996.
Krantz, S. G. “Fourier Series.” §15.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 195-202, 1999.
Lighthill, M. J. Introduction to Fourier Analysis and Generalised Functions. Cambridge, England: Cambridge University Press, 1958.
Morrison, N. Introduction to Fourier Analysis. New York: Wiley, 1994.
Sansone, G. “Expansions in Fourier Series.” Ch. 2 in Orthogonal Functions, rev. English ed. New York: Dover, pp. 39-168, 1991.
Weisstein, E. W. “Books about Fourier Transforms.” http://www.ericweisstein.com/encyclopedias/books/FourierTransforms.html.
Whittaker, E. T. and Robinson, G. “Practical Fourier Analysis.” Ch. 10 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 260-284, 1967.
From Fourier Analysis to Wavelets
Author: Jonas Gomes , Luiz Velho
Fourier Analysis and Approximation
Graduate level
• Grafakos, “Classical and Modern Fourier Analysis”
• Sogge, “Fourier Integrals in Classical Analysis”
distribution theory, and theory of partial/pseudo/para-differential operators
• Friendlander and Joschi, “Introduction to the theory of distributions”
• Hörmander, “Analysis of Linear Partial Differential Operators”
• Alinhac and Gérard, “Pseudo-differential Operators and the Nash-Moser Theorem”
Serendipities 