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

This page provides a list of all articles available at PlanetMath in the following topic:

42-XX Fourier analysis.

This list will be periodically updated. Each entry in the list has three fields:

1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:

Status	means PM article
N	not needed
A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

• Please update the WP and Status fields as appropriate.
• if the WP field is correct please remove the qualifier "guess".
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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=9764^new! -- 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=8698^new! -- WP guess: existence of Laplace transform -- Status:

• PM: Laplace transform of a Gaussian function, id=8108^new! -- 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=7641^new! -- WP guess: common Fourier series -- Status:

• PM: generalized Riemann-Lebesgue lemma, id=9398^new! -- 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=9748^new! -- 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=8637^new! -- WP guess: approximating Fourier integrals with discrete Fourier transforms -- Status:

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

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

• PM: proof of sampling theorem, id=8650^new! -- 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=7920^new! -- WP guess: Ingham Inequality -- Status:

• PM: proof of Ingham Inequality, id=7928^new! -- 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)