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== References == {{refbegin|2|indent=yes}} <!-- DO NOT leave blank lines between list items, they create entirely new lists --> * {{citation | last1 = Arfken | first1 = George | title = Mathematical Methods for Physicists | date = 1985 | publisher = Academic Press | isbn = 9780120598205 | edition = 3rd }} * {{citation | last1 = Bailey | first1 = David H. | last2 = Swarztrauber | first2 = Paul N. | title = A fast method for the numerical evaluation of continuous Fourier and Laplace transforms | journal = [[SIAM Journal on Scientific Computing]] | volume = 15 | issue = 5 | year = 1994 | pages = 1105–1110 | doi = 10.1137/0915067 | bibcode = 1994SJSC...15.1105B | url = http://crd.lbl.gov/~dhbailey/dhbpapers/fourint.pdf | citeseerx = 10.1.1.127.1534 | access-date = 2017-11-01 | archive-date = 2008-07-20 | archive-url = https://web.archive.org/web/20080720002714/http://crd.lbl.gov/~dhbailey/dhbpapers/fourint.pdf | url-status = dead }} * {{citation | last=Billingsley | first=Patrick | title=Probability and measure | publisher=Wiley | publication-place=New York, NY | date=1995 | isbn=978-0-471-00710-4}} * {{citation | editor-last = Boashash | editor-first = B. | title = Time–Frequency Signal Analysis and Processing: A Comprehensive Reference | publisher = Elsevier Science | location = Oxford | year = 2003 | isbn = 978-0-08-044335-5 }} * {{citation | last1 = Bochner | first1 = S. | author1-link = Salomon Bochner | last2 = Chandrasekharan | first2 = K. | author2-link = K. S. Chandrasekharan | title = Fourier Transforms | publisher = [[Princeton University Press]] | year = 1949 }} * {{citation | last = Bracewell | first = R. N. | title = The Fourier Transform and Its Applications | edition = 3rd | location = Boston | publisher = McGraw-Hill | year = 2000 | isbn = 978-0-07-116043-8 }} * {{citation | last1 = Campbell | first1 = George | last2 = Foster | first2 = Ronald | title = Fourier Integrals for Practical Applications | publisher = D. Van Nostrand Company, Inc. | location = New York | year = 1948 }} * {{citation | last1 = Celeghini | first1 = Enrico | last2 = Gadella | first2 = Manuel | last3 = del Olmo | first3 = Mariano A. | journal = Symmetry | date = 2021 | volume = 13 | issue = 5 | title = Hermite Functions and Fourier Series | page = 853 | doi = 10.3390/sym13050853 | arxiv = 2007.10406 | bibcode = 2021Symm...13..853C | doi-access = free }} * {{citation | last = Champeney | first = D.C. | title = A Handbook of Fourier Theorems | year = 1987 | publisher = [[Cambridge University Press]] | bibcode = 1987hft..book.....C }} * {{citation | last = Chatfield | first = Chris | title = The Analysis of Time Series: An Introduction | year = 2004 | edition = 6th | publisher = Chapman & Hall/CRC | series = Texts in Statistical Science | location = London | isbn = 9780203491683 | url = https://books.google.com/books?id=qKzyAbdaDFAC&q=%22Fourier+transform%22 }} * {{citation | last1 = Clozel | first1 = Laurent | last2 = Delorme | first2 = Patrice | title = Sur le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs réels | date = 1985 | journal = Comptes Rendus de l'Académie des Sciences, Série I | volume = 300 | pages = 331–333 }} * {{citation | last = Condon | first = E. U. | author-link = Edward Condon | title = Immersion of the Fourier transform in a continuous group of functional transformations | journal = [[PNAS|Proc. Natl. Acad. Sci.]] | volume = 23 | issue = 3 | pages = 158–164 | year = 1937 | doi=10.1073/pnas.23.3.158 | pmid = 16588141 | pmc = 1076889 | bibcode = 1937PNAS...23..158C | doi-access = free }} * {{citation | last1 = de Groot | first1 = Sybren R. | last2 = Mazur | first2 = Peter | title = Non-Equilibrium Thermodynamics | edition = 2nd | year = 1984 | publisher = [[Dover Publications|Dover]] | location = New York }} * {{citation | last = Duoandikoetxea | first = Javier | title = Fourier Analysis | publisher = [[American Mathematical Society]] | year = 2001 | isbn = 978-0-8218-2172-5 }} * {{citation | last1 = Dym | first1 = H. | author1-link = Harry Dym | last2 = McKean | first2 = H. | title = Fourier Series and Integrals | publisher = [[Academic Press]] | year = 1985 | isbn = 978-0-12-226451-1 }} * {{citation | last = Easton | first = Roger L. Jr. | title = Fourier Methods in Imaging | date = 2010 | publisher = John Wiley & Sons | isbn = 978-0-470-68983-7 | url = https://books.google.com/books?id=wCoDDQAAQBAJ | access-date = 26 May 2020 | language = en }} * {{cite book | last=Edwards | first=R. E. | title=Fourier Series | series=Graduate Texts in Mathematics | publisher=Springer New York | publication-place=New York, NY | volume=64 | date=1979 | isbn=978-1-4612-6210-7 | doi=10.1007/978-1-4612-6208-4}} * {{cite book | last=Edwards | first=R. E. | title=Fourier Series | series=Graduate Texts in Mathematics | publisher=Springer New York | publication-place=New York, NY | volume=85 | date=1982 | isbn=978-1-4613-8158-7 | doi=10.1007/978-1-4613-8156-3}} * {{citation | editor-last = Erdélyi | editor-first = Arthur | title = Tables of Integral Transforms | volume = 1 | publisher = McGraw-Hill | year = 1954 }} * {{citation | last = Feller | first = William | author-link = William Feller | title = An Introduction to Probability Theory and Its Applications | volume = II | publisher = [[John Wiley & Sons|Wiley]] | location = New York | edition = 2nd | mr = 0270403 | year = 1971 }} * {{citation | last = Folland | first = Gerald | title = Harmonic analysis in phase space | publisher = [[Princeton University Press]] | year = 1989 }} * {{citation | last = Folland | first = Gerald | title = Fourier analysis and its applications | publisher = [[Wadsworth & Brooks/Cole]] | year = 1992 }} * {{citation | last = Fourier | first = J.B. Joseph | author-link = Joseph Fourier | title = Théorie analytique de la chaleur | location = Paris | url = https://books.google.com/books?id=TDQJAAAAIAAJ&q=%22c%27est-%C3%A0-dire+qu%27on+a+l%27%C3%A9quation%22&pg=PA525 | publisher = Firmin Didot, père et fils | year = 1822 | language = fr | oclc = 2688081 }} * {{citation | last = Fourier | first = J.B. Joseph | author-link = Joseph Fourier | title = The Analytical Theory of Heat | journal = Nature | url = https://books.google.com/books?id=-N8EAAAAYAAJ&q=%22that+is+to+say%2C+that+we+have+the+equation%22&pg=PA408 | year = 1878 | volume = 18 | issue = 451 | page = 192 | orig-year = 1822 | publisher = The University Press | doi = 10.1038/018192a0 | bibcode = 1878Natur..18Q.192. | translator = Alexander Freeman }} (translated from French) * {{citation | last1 = Gradshteyn | first1 = Izrail Solomonovich | author1-link = Izrail Solomonovich Gradshteyn | last2 = Ryzhik | first2 = Iosif Moiseevich | author2-link = Iosif Moiseevich Ryzhik | last3 = Geronimus | first3 = Yuri Veniaminovich | author3-link = Yuri Veniaminovich Geronimus | last4 = Tseytlin | first4 = Michail Yulyevich | author4-link = Michail Yulyevich Tseytlin | last5 = Jeffrey | first5 = Alan | editor1-last = Zwillinger | editor1-first = Daniel | editor2-last = Moll | editor2-first = Victor Hugo | editor-link2=Victor Hugo Moll | translator = Scripta Technica, Inc. | title = Table of Integrals, Series, and Products | title-link = Gradshteyn and Ryzhik | publisher = [[Academic Press]] | year = 2015 | edition = 8th | language = en | isbn = 978-0-12-384933-5 }} * {{citation | last = Grafakos | first = Loukas | title = Classical and Modern Fourier Analysis | publisher = Prentice-Hall | year = 2004 | isbn = 978-0-13-035399-3 }} * {{citation | last1 = Grafakos | first1 = Loukas | last2 = Teschl | first2 = Gerald | author2-link = Gerald Teschl | title = On Fourier transforms of radial functions and distributions | journal = J. Fourier Anal. Appl. | volume = 19 | pages = 167–179 | year = 2013 | issue = 1 | doi = 10.1007/s00041-012-9242-5 | arxiv = 1112.5469 | bibcode = 2013JFAA...19..167G | s2cid = 1280745 }} * {{citation | last1 = Greiner | first1 = W. | last2 = Reinhardt | first2 = J. | title = Field Quantization | publisher = [[Springer-Verlag|Springer]] | year = 1996 | isbn = 978-3-540-59179-5 | url-access = registration | url = https://archive.org/details/fieldquantizatio0000grei }} * {{citation | last1 = Gelfand | first1 = I.M. | author1-link = Israel Gelfand | last2 = Shilov | first2 = G.E. | author2-link = Naum Ya. Vilenkin | title = Generalized Functions | volume = 1 | publisher = [[Academic Press]] | location = New York | year = 1964 }} (translated from Russian) * {{citation | last1 = Gelfand | first1 = I.M. | author1-link = Israel Gelfand | last2 = Vilenkin | first2 = N.Y. | author2-link = Naum Ya. Vilenkin | title = Generalized Functions | volume = 4 | publisher = [[Academic Press]] | location = New York | year = 1964 }} (translated from Russian) * {{citation | last1 = Hewitt | first1 = Edwin | last2 = Ross | first2 = Kenneth A. | title = Abstract harmonic analysis | volume = II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups | publisher = [[Springer-Verlag|Springer]] | series = Die Grundlehren der mathematischen Wissenschaften, Band 152 | mr = 0262773 | year = 1970 }} * {{citation | last = Hörmander | first = L. | author-link = Lars Hörmander | title = Linear Partial Differential Operators | volume = 1 | publisher = [[Springer-Verlag|Springer]] | year = 1976 | isbn = 978-3-540-00662-6 }} * {{citation | last = Howe | first = Roger | title= On the role of the Heisenberg group in harmonic analysis | journal = [[Bulletin of the American Mathematical Society]] | volume = 3 | pages = 821–844 | number = 2 | year = 1980 | doi = 10.1090/S0273-0979-1980-14825-9 | mr = 578375 | doi-access = free }} * {{citation | last = Hunter | first = J.K. | title = Appendix: The Fourier transform | work = Lecture Notes on PDEs | url = https://www.math.ucdavis.edu/~hunter/pdes/pdes.html | access-date = January 12, 2025 | year = 2014 }} * {{citation | last = James | first = J.F. | title = A Student's Guide to Fourier Transforms | edition = 3rd | publisher = [[Cambridge University Press]] | year = 2011 | bibcode = 2011sgft.book.....J | isbn = 978-0-521-17683-5 }} * {{citation | last = Jordan | first = Camille | author-link = Camille Jordan | title = Cours d'Analyse de l'École Polytechnique | volume = II, Calcul Intégral: Intégrales définies et indéfinies | edition = 2nd | location = Paris | year = 1883 }} * {{citation | last = Kaiser | first = Gerald | title = A Friendly Guide to Wavelets | journal = Physics Today | volume = 48 | issue = 7 | pages = 57–58 | year = 1994 | isbn = 978-0-8176-3711-8 | url = https://books.google.com/books?id=rfRnrhJwoloC&q=%22becomes+the+Fourier+%28integral%29+transform%22&pg=PA29 | bibcode = 1995PhT....48g..57K | doi = 10.1063/1.2808105 }} * {{citation | last = Kammler | first = David | title = A First Course in Fourier Analysis | year = 2000 | publisher = Prentice Hall | isbn = 978-0-13-578782-3 }} * {{citation | last=Katznelson | first=Yitzhak | title=An Introduction to Harmonic Analysis | publisher=Cambridge University Press | date=2004 | isbn=978-0-521-83829-0 | doi=10.1017/cbo9781139165372 | url=https://www.cambridge.org/core/product/identifier/9781139165372/type/book}} * {{citation | last1 = Khare | first1 = Kedar | last2 = Butola | first2 = Mansi | last3 = Rajora | first3 = Sunaina | title = Fourier Optics and Computational Imaging | publisher = Springer | year = 2023 | isbn = 978-3-031-18353-9 | edition = 2nd | chapter = Chapter 2.3 Fourier Transform as a Limiting Case of Fourier Series | doi = 10.1007/978-3-031-18353-9 | s2cid = 255676773 }} * {{citation | last1 = Kirillov | first1 = Alexandre | author1-link = Alexandre Kirillov | last2 = Gvishiani | first2 = Alexei D. | title = Theorems and Problems in Functional Analysis | year = 1982 | orig-year = 1979 | publisher = [[Springer-Verlag|Springer]] }} (translated from Russian) * {{citation | last = Knapp | first = Anthony W. | title = Representation Theory of Semisimple Groups: An Overview Based on Examples | url = https://books.google.com/books?id=QCcW1h835pwC | publisher = [[Princeton University Press]] | year = 2001 | isbn = 978-0-691-09089-4 }} * {{citation | last1 = Kolmogorov | first1 = Andrey Nikolaevich | author1-link = Andrey Kolmogorov | last2 = Fomin | first2 = Sergei Vasilyevich | author2-link = Sergei Fomin | title = Elements of the Theory of Functions and Functional Analysis | year = 1999 | orig-year = 1957 | publisher = [[Dover Publications|Dover]] | url = http://store.doverpublications.com/0486406830.html }} (translated from Russian) * {{citation | last = Lado | first = F. | title = Numerical Fourier transforms in one, two, and three dimensions for liquid state calculations | journal = [[Journal of Computational Physics]] | volume = 8 | issue = 3 | year = 1971 | pages = 417–433 | doi = 10.1016/0021-9991(71)90021-0 | bibcode = 1971JCoPh...8..417L | url = http://www.lib.ncsu.edu/resolver/1840.2/2465 }} * {{citation| last=Mallat | first=Stéphane | authorlink=Stephane Mallat| title=A wavelet tour of signal processing: the sparse way | publisher=Elsevier/Academic Press | publication-place=Amsterdam Boston | date=2009 | doi=10.1016/B978-0-12-374370-1.X0001-8|isbn=978-0-12-374370-1}} * {{citation | last = Müller | first = Meinard | title = The Fourier Transform in a Nutshell. | url = https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/04-bookFMP/2015_Mueller_FundamentalsMusicProcessing_Springer_Section2-1_SamplePages.pdf | publisher = [[Springer-Verlag|Springer]] | year = 2015 | doi = 10.1007/978-3-319-21945-5 | isbn = 978-3-319-21944-8 | s2cid = 8691186 | access-date = 2016-03-28 | archive-date = 2016-04-08 | archive-url = https://web.archive.org/web/20160408083515/https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/04-bookFMP/2015_Mueller_FundamentalsMusicProcessing_Springer_Section2-1_SamplePages.pdf | url-status = dead }}; 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