Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis: Difference between revisions
Content deleted Content added
fix bug. Summary of prev edit:Added MathMartin's mention about copying an article from PM |
Remove duplicates and change status line, as per Wikipedia talk:WikiProject Mathematics |
||
Line 6:
::PM article is a proof which is not included in WP; WP doesn't even define the ''order'' of a distribution. [[User:Jitse Niesen|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4473 \operatorname{p.\!v.}(\frac{1}{x}) is a distribution of first order], id=4473 -- WP: [[distribution]] -- Status:
::PM article is a proof which is not included in WP; p.v. (1/x) is a nice example of a distribution which should be mentioned in WP. Connection with [[renormalization]]? [[User:Jitse Niesen|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4425 balanced set], id=4425 -- WP guess: [[balanced set]] -- Status: '''
::No WP article, could perhaps be included in [[Fréchet space]]. [[User:Jitse Niesen|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4426 bounded function], id=4426 -- WP: [[bounded]], [[bounded function]], [[Banach space]] -- Status: '''
::PM definition is included in [[bounded]], while [[bounded function]] uses a different definition coming from order theory. The space of bounded functions is treated as an example in [[Banach space]]. [[User:Jitse Niesen|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4429 bounded set (in a topological vector space)], id=4429 -- WP: [[bounded set]], [[bounded set (topological vector space)]] -- Status: '''
::PM definition is more general. Need to create article [[bounded set]], possibly as a redirect to bounded. The thm in PM (compact implies bounded) should be added. [[User:Jitse Niesen|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC)
:::I recently split the page from [[bounded set]] and added the theorem from PM. [[User:MathMartin|MathMartin]] 11:49, 4 May 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4472 Cauchy principal part integral], id=4472 -- WP guess: [[Cauchy principal part integral]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6195 Cauchy sequence], id=6195 -- WP: [[Cauchy sequence]] -- Status: '''
::Our artilcle is more complete. [[User:Paul August|Paul August ]] [[User_talk:Paul August|☎]] 15:03, Jan 31, 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4570 cone], id=4570 -- WP guess: [[cone]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4468 delta distribution], id=4468 -- WP guess: [[delta distribution]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4427 distribution], id=4427 -- WP guess: [[distribution]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4433 every locally integrable function is a distribution], id=4433 -- WP guess: [[every locally integrable function is a distribution]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5556 function spaces], id=5556 -- WP guess: [[function spaces]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4477 localization for distributions], id=4477 -- WP guess: [[localization for distributions]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4424 locally convex topological vector space], id=4424 -- WP guess: [[locally convex topological vector space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4440 operations on distributions], id=4440 -- WP guess: [[operations on distributions]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4437 proof of convergence theorem], id=4437 -- WP guess: [[proof of convergence theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4525 sequential characterization of boundedness], id=4525 -- WP guess: [[sequential characterization of boundedness]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4568 smooth distribution], id=4568 -- WP guess: [[smooth distribution]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4484 support of distribution], id=4484 -- WP guess: [[support of distribution]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4528 symmetric set], id=4528 -- WP guess: [[symmetric set]] -- Status:
==46A03 General theory of locally convex spaces==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5921 Krein-Milman theorem], id=5921 -- WP guess: [[Krein-Milman theorem]] -- Status:
==46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B r$-completeness)==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3702 closed graph theorem], id=3702 -- WP guess: [[closed graph theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3675 open mapping theorem], id=3675 -- WP guess: [[open mapping theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6472 proof of closed graph theorem], id=6472 -- WP guess: [[proof of closed graph theorem]] -- Status:
==46A55 Convex sets in topological linear spaces; Choquet theory==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4443 convex hull of S is open if S is open], id=4443 -- WP guess: [[convex hull of S is open if S is open]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5587 proof that the convex hull of S is open if S is open], id=5587 -- WP guess: [[proof that the convex hull of S is open if S is open]] -- Status:
==46A99 Miscellaneous==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3066 Heine-Cantor theorem], id=3066 -- WP guess: [[Heine-Cantor theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4114 proof of Heine-Cantor theorem], id=4114 -- WP guess: [[proof of Heine-Cantor theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1744 topological vector space], id=1744 -- WP guess: [[topological vector space]] -- Status:
==46B03 Isomorphic theory (including renorming) of Banach spaces==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4315 hyperbolic isomorphism], id=4315 -- WP guess: [[hyperbolic isomorphism]] -- Status:
==46B07 Local theory of Banach spaces==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5927 Lipschitz inverse mapping theorem], id=5927 -- WP guess: [[Lipschitz inverse mapping theorem]] -- Status:
==46B10 Duality and reflexivity==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6471 Banach-Alaoglu theorem], id=6471 -- WP guess: [[Banach-Alaoglu theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5229 weak* convergence in normed linear space], id=5229 -- WP guess: [[weak* convergence in normed linear space]] -- Status:
==46B20 Geometry and structure of normed linear spaces==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5399 \lim_{p \to \infty} \lVert x \rVert_p = \lVert x \rVert_{\infty}], id=5399 -- WP guess: [[\lim_p \to \infty \lVert x \rVert_p = \lVert x \rVert_\infty]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6611 Banach-Mazur compactum], id=6611 -- WP guess: [[Banach-Mazur compactum]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6240 basic properties of seminorms], id=6240 -- WP guess: [[basic properties of seminorms]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3252 Hahn-Banach theorem], id=3252 -- WP guess: [[Hahn-Banach theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6515 Minkowski's function], id=6515 -- WP guess: [[Minkowski's function]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4127 proof of Hahn-Banach theorem], id=4127 -- WP guess: [[proof of Hahn-Banach theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2322 seminorm], id=2322 -- WP guess: [[seminorm]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=91 vector norm], id=91 -- WP guess: [[vector norm]] -- Status:
==46B25 Classical Banach spaces in the general theory==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6270 proof that L^p spaces are complete], id=6270 -- WP guess: [[proof that L^p spaces are complete]] -- Status:
==46B50 Compactness in Banach (or normed) spaces==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4457 proof of Schauder fixed point theorem], id=4457 -- WP guess: [[proof of Schauder fixed point theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4455 Schauder fixed point theorem], id=4455 -- WP guess: [[Schauder fixed point theorem]] -- Status:
==46B99 Miscellaneous==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1929 \ell^p], id=1929 -- WP guess: [[\ell^p]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5564 all norms on finite-dimensional vector spaces are equivalent], id=5564 -- WP guess: [[all norms on finite-dimensional vector spaces are equivalent]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1605 Banach space], id=1605 -- WP guess: [[Banach space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6469 Banach-Steinhaus theorem], id=6469 -- WP guess: [[Banach-Steinhaus theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5226 bounded operator], id=5226 -- WP guess: [[bounded operator]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5966 compact operator], id=5966 -- WP guess: [[compact operator]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3741 continuous linear mapping], id=3741 -- WP guess: [[continuous linear mapping]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4312 equivalent norms], id=4312 -- WP guess: [[equivalent norms]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6633 every finite dimensional normed vector space is a Banach space], id=6633 -- WP guess: [[every finite dimensional normed vector space is a Banach space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6632 every subspace of a normed space of finite dimension is closed], id=6632 -- WP guess: [[every subspace of a normed space of finite dimension is closed]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1604 normed vector space], id=1604 -- WP guess: [[normed vector space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6470 proof of Banach-Steinhaus theorem], id=6470 -- WP guess: [[proof of Banach-Steinhaus theorem]] -- Status:
==46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3089 Bessel inequality], id=3089 -- WP guess: [[Bessel inequality]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6364 direct integral of Hilbert spaces], id=6364 -- WP guess: [[direct integral of Hilbert spaces]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6363 direct sum of Hilbert spaces], id=6363 -- WP guess: [[direct sum of Hilbert spaces]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3401 Hilbert module], id=3401 -- WP guess: [[Hilbert module]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6229 Hilbert parallelotope], id=6229 -- WP guess: [[Hilbert parallelotope]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1930 Hilbert space], id=1930 -- WP guess: [[Hilbert space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3090 proof of Bessel inequality], id=3090 -- WP guess: [[proof of Bessel inequality]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6239 Rellich selection theorem], id=6239 -- WP guess: [[Rellich selection theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5963 Riesz sequence], id=5963 -- WP guess: [[Riesz sequence]] -- Status:
==46C15 Characterizations of Hilbert spaces==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1933 classification of separable Hilbert spaces], id=1933 -- WP guess: [[classification of separable Hilbert spaces]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6127 proof of classification of separable Hilbert spaces], id=6127 -- WP guess: [[proof of classification of separable Hilbert spaces]] -- Status:
==46C99 Miscellaneous==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5969 characterization of tight frames in {\mathbb R}^n], id=5969 -- WP guess: [[characterization of tight frames in \mathbb R^n]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5935 frame], id=5935 -- WP guess: [[frame]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5961 multiresolution analysis], id=5961 -- WP guess: [[multiresolution analysis]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6130 proof of Riesz representation theorem for separable Hilbert spaces], id=6130 -- WP guess: [[proof of Riesz representation theorem for separable Hilbert spaces]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5585 Riesz representation theorem], id=5585 -- WP guess: [[Riesz representation theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5586 Riesz-Fischer theorem], id=5586 -- WP guess: [[Riesz-Fischer theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5984 set of sampling], id=5984 -- WP guess: [[set of sampling]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5959 wavelet], id=5959 -- WP guess: [[wavelet]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5971 wavelet set], id=5971 -- WP guess: [[wavelet set]] -- Status:
==46E15 Banach spaces of continuous, differentiable or analytic functions==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2961 Ascoli-Arzelà theorem], id=2961 -- WP guess: [[Ascoli-Arzelà theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3753 proof of Ascoli-Arzelà theorem], id=3753 -- WP guess: [[proof of Ascoli-Arzelà theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6146 proof of Stone-Weierstrass theorem], id=6146 -- WP guess: [[proof of Stone-Weierstrass theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2984 Stone-Weierstrass theorem], id=2984 -- WP guess: [[Stone-Weierstrass theorem]] -- Status:
==46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2051 conjugate index], id=2051 -- WP guess: [[conjugate index]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=94 Holder inequality], id=94 -- WP guess: [[Holder inequality]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4110 proof of Holder inequality], id=4110 -- WP guess: [[proof of Holder inequality]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4079 proof of Young Inequality], id=4079 -- WP guess: [[proof of Young Inequality]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4078 Young Inequality], id=4078 -- WP guess: [[Young Inequality]] -- Status:
==46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6601 Sobolev space], id=6601 -- WP guess: [[Sobolev space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6600 weak derivative], id=6600 -- WP guess: [[weak derivative]] -- Status:
==46E40 Spaces of vector- and operator-valued functions==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=902 vector field], id=902 -- WP guess: [[vector field]] -- Status:
==46F05 Topological linear spaces of test functions, distributions and ultradistributions==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=
* PM: [http://planetmath.org/?op=getobj&from=objects&id=
==46G05 Derivatives==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2975 derivative], id=2975 -- WP guess: [[derivative]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6395 higher order derivatives of sine and cosine], id=6395 -- WP guess: [[higher order derivatives of sine and cosine]] -- Status:
==46H05 General theory of topological algebras==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3333 Banach algebra], id=3333 -- WP guess: [[Banach algebra]] -- Status:
==46H35 Topological algebras of operators==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6402 topological *-algebra], id=6402 -- WP guess: [[topological *-algebra]] -- Status:
==46K05 General theory of topological algebras with involution==
==46L05 General theory of $C^*$-algebras==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3334 C^*-algebra], id=3334 -- WP guess: [[C^*-algebra]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6438 bounded operators on a Hilbert space form a C^*-algebra], id=6438 -- WP guess: [[bounded operators on a Hilbert space form a C^*-algebra]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3335 Gelfand-Naimark representation theorem], id=3335 -- WP guess: [[Gelfand-Naimark representation theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4574 state], id=4574 -- WP guess: [[state]] -- Status:
==46L85 Noncommutative topology==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4065 Gelfand-Naimark theorem], id=4065 -- WP guess: [[Gelfand-Naimark theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4066 Serre-Swan theorem], id=4066 -- WP guess: [[Serre-Swan theorem]] -- Status:
==46L87 Noncommutative differential geometry==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3329 Fredholm module], id=3329 -- WP guess: [[Fredholm module]] -- Status:
==46M05 Tensor products==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=899 triple scalar product], id=899 -- WP guess: [[triple scalar product]] -- Status:
==46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds==
| |||