Editing Incubator escapee wiki:WikiProject Mathematics/PlanetMath Exchange/42-XX Fourier analysis

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{{Planetmath instructions|topic=42-XX Fourier analysis}}

==42-00 General reference works (handbooks, dictionaries, bibliographies, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=1469 discrete cosine transform], id=1469 -- WP: [[discrete cosine transform]] -- Status: '''A'''
::[[User:CryptoDerk|CryptoDerk]] 21:27, Feb 2, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9764 discrete sine transform], id=9764<sup><span style="color:red;">new!</span></sup> -- WP guess: [[discrete sine transform]] -- Status:

==42-01 Instructional exposition (textbooks, tutorial papers, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4343 Laplace transform], id=4343 -- WP: [[Laplace transform]] -- Status: '''A'''
::[[User:CryptoDerk|CryptoDerk]] 21:37, Feb 2, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8698 existence of Laplace transform], id=8698<sup><span style="color:red;">new!</span></sup> -- WP guess: [[existence of Laplace transform]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8108 Laplace transform of a Gaussian function], id=8108<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Laplace transform of a Gaussian function]] -- Status:

==42A05 Trigonometric polynomials, inequalities, extremal problems==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=2161 Chebyshev polynomial], id=2161 -- WP: [[Chebyshev polynomial]] -- Status: '''A'''
::[[User:CryptoDerk|CryptoDerk]] 21:59, Feb 2, 2005 (UTC)

==42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4718 example of Fourier series], id=4718 -- WP: [[Fourier series]] -- Status: '''M'''
::[[User:CryptoDerk|CryptoDerk]] 23:05, Feb 2, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3571 Riemann-Lebesgue lemma], id=3571 -- WP: [[Riemann-Lebesgue lemma]] -- Status: '''C'''
::[[User:CryptoDerk|CryptoDerk]] 01:56, Feb 3, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7641 common Fourier series], id=7641<sup><span style="color:red;">new!</span></sup> -- WP guess: [[common Fourier series]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9398 generalized Riemann-Lebesgue lemma], id=9398<sup><span style="color:red;">new!</span></sup> -- WP guess: [[generalized Riemann-Lebesgue lemma]] -- Status:

==42A20 Convergence and absolute convergence of Fourier and trigonometric series==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3891 Dirichlet conditions], id=3891 -- WP: [[Dirichlet conditions]] -- Status: '''A'''
::The PM article is actually fairly ambiguous.  It states truths, but doesn't really give a hard definition for the conditions.  [[User:CryptoDerk|CryptoDerk]] 02:31, Feb 3, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9748 Wiener algebra], id=9748<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Wiener algebra]] -- Status:

==42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=2823 Fourier transform], id=2823 -- WP: [[Fourier transform]] -- Status: '''A'''
::Kind of spread out amongst various articles, including [[continuous Fourier transform]] and related articles linked to from the main [[Fourier transform]] article.  [[User:CryptoDerk|CryptoDerk]] 02:51, Feb 3, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8637 approximating Fourier integrals with discrete Fourier transforms], id=8637<sup><span style="color:red;">new!</span></sup> -- WP guess: [[approximating Fourier integrals with discrete Fourier transforms]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8785 microlocal analysis], id=8785<sup><span style="color:red;">new!</span></sup> -- WP guess: [[microlocal analysis]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8651 Plancherel's theorem], id=8651<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Plancherel's theorem]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8650 proof of sampling theorem], id=8650<sup><span style="color:red;">new!</span></sup> -- WP guess: [[proof of sampling theorem]] -- Status:

==42A75 Classical almost periodic functions, mean periodic functions==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6567 almost periodic function], id=6567 -- WP: [[almost periodic function]] -- Status: '''A'''
::[[User:CryptoDerk|CryptoDerk]] 02:54, Feb 3, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7214 almost periodic function (equivalent definition)], id=7214 -- WP: [[almost periodic function]] -- Status: '''A'''
::Added to WP article some content motivated by this PM article. [[User:Bjcairns|Ben Cairns]] 11:29, 18 April 2006 (UTC)

==42A99 Miscellaneous==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4022 Poisson summation formula], id=4022 -- WP: [[Poisson summation formula]] -- Status: '''NM'''
::Entry is locked on PM. The author states "The reason that the entry is now inaccessible, when I adopted it from the orphanage, the proof contains serious errors, so I turned off access to it until I had a chance to replace it with a correct proof. This was done so that noone would be misled by an erroneous entry. I had left the project of repairing this proof on the back burner for a while, but now I will get back to it. As soon as I am done, I will make the entry accessible again and let you know." [[User:CryptoDerk|CryptoDerk]] 04:33, Feb 3, 2005 (UTC)
::A new proof is now available on PM.  [[User:Bjcairns|Ben Cairns]] 12:53, 18 April 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=5993 progressive function], id=5993 -- WP: [[progressive function]] -- Status: '''C'''
::[[User:CryptoDerk|CryptoDerk]] 03:24, Feb 3, 2005 (UTC)

==42Axx Fourier analysis in one variable==

==42B05 Fourier series and coefficients==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4717 Parseval equality], id=4717 -- WP: [[Parseval's theorem]] -- Status: '''A'''
::[[User:CryptoDerk|CryptoDerk]] 03:44, Feb 3, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=5393 Wirtinger's inequality], id=5393 -- WP: [[Wirtinger's inequality]] -- Status: '''C'''
::[[User:CryptoDerk|CryptoDerk]] 03:59, Feb 3, 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7920 Ingham Inequality], id=7920<sup><span style="color:red;">new!</span></sup> -- WP guess: [[Ingham Inequality]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7928 proof of Ingham Inequality], id=7928<sup><span style="color:red;">new!</span></sup> -- WP guess: [[proof of Ingham Inequality]] -- Status:

==42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type==

==42Bxx Fourier analysis in several variables==

==42C05 Orthogonal functions and polynomials, general theory==

==42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7497 Balian-Low], id=7497 -- WP: [[Balian-Low theorem]] -- Status: '''C'''
::[[User:Bjcairns|Ben Cairns]] 12:03, 18 April 2006 (UTC)

==42C99 Miscellaneous==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7152 an equivalent condition for the translates of an L_2 function to form a Riesz basis], id=7152 -- WP: [[Riesz sequence]] -- Status: '''C'''
::Copied both Riesz sequence and Riesz basis to WP article.  [[User:Bjcairns|Ben Cairns]] 12:46, 18 April 2006 (UTC)

==42Cxx Nontrigonometric Fourier analysis==