In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin...
4 KB (562 words) - 14:34, 19 March 2025
In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping)...
1 KB (154 words) - 14:43, 19 March 2025
itself; this established the Riemann mapping theorem. Constantin Carathéodory gave another proof of the theorem in 1912, which was the first to rely purely...
44 KB (7,478 words) - 16:34, 20 May 2025
Schoenflies problem (redirect from Jordan–Schönflies theorem)
Jordan-Schoenflies Theorem", Proceedings of the American Mathematical Society, 2 (6): 860–867, doi:10.1090/S0002-9939-1951-0046635-9, MR 0046635 Carathéodory, Constantin...
30 KB (4,226 words) - 11:59, 26 September 2024
Bôcher's theorem (complex analysis) Borel–Carathéodory theorem (complex analysis) Branching theorem (complex manifold) Carathéodory's theorem (complex...
78 KB (6,289 words) - 12:34, 6 June 2025
Dirac delta function (section The heat kernel)
representation theorem, is represented by integration against a kernel K z ( ζ ) {\displaystyle K_{z}(\zeta )} , the Bergman kernel. This kernel is the analog...
96 KB (14,230 words) - 04:36, 14 May 2025
Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex...
20 KB (2,957 words) - 18:17, 16 April 2025
Planar Riemann surface (section Uniformization theorem)
"Kreisnormierungs" theorem. Following Goluzin (1969) it can be deduced from the parallel slit theorem using a variant of Carathéodory's kernel theorem and Brouwer's...
38 KB (5,243 words) - 07:52, 21 January 2025
Positive harmonic function (redirect from Herglotz representation theorem)
_{m}{\overline {\lambda _{n}}}=2(1-|z|^{2})\,\Re \,f(z).} Bochner's theorem Carathéodory, C. (1907), "Über den Variabilitätsbereich der Koeffizienten von...
5 KB (861 words) - 18:54, 8 April 2025
theorem there is a conformal mapping fn of Ωn onto Ω, normalised to fix a given point in Ω with positive derivative there. By the Carathéodory kernel...
4 KB (560 words) - 05:14, 2 March 2024
sense of the Carathéodory kernel theorem. If D {\displaystyle D} denotes the unit disk in C {\displaystyle \mathbb {C} } , this theorem implies that the...
13 KB (2,606 words) - 08:17, 21 January 2025
David Hilbert (section Theorems)
Hilbert–Burch theorem Hilbert's irreducibility theorem Hilbert's Nullstellensatz Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Hilbert's...
60 KB (7,098 words) - 10:15, 8 June 2025
F|∂Ωs have bounded norm in L2(∂Ω). An argument based on the Carathéodory kernel theorem shows that this condition is satisfied whenever there is a family...
29 KB (5,037 words) - 03:40, 30 November 2024
A generalized sphere theorem. Ann. of Math. (2) 106 (1977), no. 2, 201–211. Li, Peter; Yau, Shing-Tung. On the parabolic kernel of the Schrödinger operator...
48 KB (3,749 words) - 17:22, 27 May 2025
differential operator of order n, Carathéodory's existence theorem implies that, under very mild conditions, the kernel of L is a vector space of dimension...
30 KB (4,754 words) - 02:35, 2 May 2025
Lagrange multiplier (redirect from Lagrange multiplier theorem)
In nonlinear programming there are several multiplier rules, e.g. the Carathéodory–John Multiplier Rule and the Convex Multiplier Rule, for inequality constraints...
52 KB (7,988 words) - 15:06, 24 May 2025
Fourier series. Fejér collaborated to produce important papers, one with Carathéodory on entire functions in 1907 and another major work with Frigyes Riesz...
13 KB (1,288 words) - 21:06, 17 January 2025
of a set is a notion in potential theory. Carathéodory 1. Carathéodory's extension theorem 2. Caratheodory's criterion states a sufficient condition for...
28 KB (4,371 words) - 05:59, 1 June 2025
Using reproducing kernel Hilbert space techniques, he gave elegant proofs of the Julia–Carathéodory and the Denjoy–Wolff theorems. Two recent accounts...
8 KB (1,025 words) - 07:26, 18 June 2024
the origin to X, i.e. f ( 0 ) = X {\displaystyle f(0)=X} . See Carathéodory's theorem. If D ⊂ R 2 {\displaystyle D\subset \mathbb {R} ^{2}} is the domain...
11 KB (1,792 words) - 02:42, 20 June 2024
spherical Bernstein's problem, a generalization of Bernstein's problem Carathéodory conjecture: any convex, closed, and twice-differentiable surface in three-dimensional...
195 KB (20,026 words) - 13:12, 7 May 2025
that | a | 2 ≤ 1 2 . {\displaystyle |a|^{2}\leq {\tfrac {1}{2}}.} Carathéodory's theorem: If S {\displaystyle S} is any subset of R n {\displaystyle \mathbb...
58 KB (10,568 words) - 16:17, 4 June 2025
vector is in the cone might be exponentially long. Fortunately, Carathéodory's theorem guarantees that every vector in the cone can be represented by at...
28 KB (3,941 words) - 12:49, 8 May 2025
differential form d U − d W {\displaystyle dU-dW} is not closed. Caratheodory's theorem further states that there exists an integrating denominator T {\displaystyle...
15 KB (2,603 words) - 23:11, 2 May 2025
Joseph A.; Graham, Ian; Kim, Kang Tae; Krantz, Steven G. The Carathéodory-Cartan-Kaup-Wu theorem on an infinite-dimensional Hilbert space. Nagoya Math. J...
13 KB (1,594 words) - 08:40, 14 November 2024
fundamental solutions. In the case of the forced dispersionless spring, the kernel sin ( t − s ) = sin t cos s − sin s cos t {\displaystyle \sin(t-s)=\sin...
21 KB (3,989 words) - 04:48, 6 December 2023
with two papers, both published in 1937: On the extension of a theorem of Caratheodory in the theory of Fourier series, and, The Fourier series of a sequence...
6 KB (557 words) - 14:21, 28 May 2025
of the Pap test), mathematician Constantin Carathéodory (known for the Carathéodory theorems and Carathéodory conjecture), astronomer E. M. Antoniadi, archaeologists...
286 KB (25,898 words) - 21:37, 7 June 2025
available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same temperature...
103 KB (13,522 words) - 10:24, 31 May 2025