Wikipedia:WikiProject Mathematics/PlanetMath Exchange/42-XX Fourier analysis

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

 * PM: discrete cosine transform, id=1469 -- WP: discrete cosine transform -- Status: A
 * CryptoDerk 21:27, Feb 2, 2005 (UTC)


 * PM: discrete sine transform, id=9764new! -- WP guess: discrete sine transform -- Status:

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

 * PM: Laplace transform, id=4343 -- WP: Laplace transform -- Status: A
 * CryptoDerk 21:37, Feb 2, 2005 (UTC)


 * PM: existence of Laplace transform, id=8698new! -- WP guess: existence of Laplace transform -- Status:


 * PM: Laplace transform of a Gaussian function, id=8108new! -- WP guess: Laplace transform of a Gaussian function -- Status:

42A05 Trigonometric polynomials, inequalities, extremal problems

 * PM: Chebyshev polynomial, id=2161 -- WP: Chebyshev polynomial -- Status: A
 * CryptoDerk 21:59, Feb 2, 2005 (UTC)

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

 * PM: example of Fourier series, id=4718 -- WP: Fourier series -- Status: M
 * CryptoDerk 23:05, Feb 2, 2005 (UTC)


 * PM: Riemann-Lebesgue lemma, id=3571 -- WP: Riemann-Lebesgue lemma -- Status: C
 * CryptoDerk 01:56, Feb 3, 2005 (UTC)


 * PM: common Fourier series, id=7641new! -- WP guess: common Fourier series -- Status:


 * PM: generalized Riemann-Lebesgue lemma, id=9398new! -- WP guess: generalized Riemann-Lebesgue lemma -- Status:

42A20 Convergence and absolute convergence of Fourier and trigonometric series

 * PM: 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.  CryptoDerk 02:31, Feb 3, 2005 (UTC)


 * PM: Wiener algebra, id=9748new! -- WP guess: Wiener algebra -- Status:

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

 * PM: 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. CryptoDerk 02:51, Feb 3, 2005 (UTC)


 * PM: approximating Fourier integrals with discrete Fourier transforms, id=8637new! -- WP guess: approximating Fourier integrals with discrete Fourier transforms -- Status:


 * PM: microlocal analysis, id=8785new! -- WP guess: microlocal analysis -- Status:


 * PM: Plancherel's theorem, id=8651new! -- WP guess: Plancherel's theorem -- Status:


 * PM: proof of sampling theorem, id=8650new! -- WP guess: proof of sampling theorem -- Status:

42A75 Classical almost periodic functions, mean periodic functions

 * PM: almost periodic function, id=6567 -- WP: almost periodic function -- Status: A
 * CryptoDerk 02:54, Feb 3, 2005 (UTC)


 * PM: almost periodic function (equivalent definition), id=7214 -- WP: almost periodic function -- Status: A
 * Added to WP article some content motivated by this PM article. Ben Cairns 11:29, 18 April 2006 (UTC)

42A99 Miscellaneous

 * PM: 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." CryptoDerk 04:33, Feb 3, 2005 (UTC)
 * A new proof is now available on PM. Ben Cairns 12:53, 18 April 2006 (UTC)


 * PM: progressive function, id=5993 -- WP: progressive function -- Status: C
 * CryptoDerk 03:24, Feb 3, 2005 (UTC)

42B05 Fourier series and coefficients

 * PM: Parseval equality, id=4717 -- WP: Parseval's theorem -- Status: A
 * CryptoDerk 03:44, Feb 3, 2005 (UTC)


 * PM: Wirtinger's inequality, id=5393 -- WP: Wirtinger's inequality -- Status: C
 * CryptoDerk 03:59, Feb 3, 2005 (UTC)


 * PM: Ingham Inequality, id=7920new! -- WP guess: Ingham Inequality -- Status:


 * PM: proof of Ingham Inequality, id=7928new! -- WP guess: proof of Ingham Inequality -- Status:

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

 * PM: Balian-Low, id=7497 -- WP: Balian-Low theorem -- Status: C
 * Ben Cairns 12:03, 18 April 2006 (UTC)

42C99 Miscellaneous

 * PM: 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. Ben Cairns 12:46, 18 April 2006 (UTC)