In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin...

In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping)...

itself; this established the Riemann mapping theorem. Constantin Carathéodory gave another proof of the theorem in 1912, which was the first to rely purely...

representation theorem, is represented by integration against a kernel K z ( ζ ) {\displaystyle K_{z}(\zeta )} , the Bergman kernel. This kernel is the analog...

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...

Bôcher's theorem (complex analysis) Borel–Carathéodory theorem (complex analysis) Branching theorem (complex manifold) Carathéodory's theorem (complex...

"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...

Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex...

_{m}{\overline {\lambda _{n}}}=2(1-|z|^{2})\,\Re \,f(z).} Bochner's theorem Carathéodory, C. (1907), "Über den Variabilitätsbereich der Koeffizienten von...

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...

sense of the Carathéodory kernel theorem. If D {\displaystyle D} denotes the unit disk in C {\displaystyle \mathbb {C} } , this theorem implies that the...

Hilbert–Burch theorem Hilbert's irreducibility theorem Hilbert's Nullstellensatz Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Hilbert's...

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...

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...

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...

In nonlinear programming there are several multiplier rules, e.g. the Carathéodory–John Multiplier Rule and the Convex Multiplier Rule, for inequality constraints...

Fourier series. Fejér collaborated to produce important papers, one with Carathéodory on entire functions in 1907 and another major work with Frigyes Riesz...

of a set is a notion in potential theory. Carathéodory 1.  Carathéodory's extension theorem 2.  Caratheodory's criterion states a sufficient condition for...

Using reproducing kernel Hilbert space techniques, he gave elegant proofs of the Julia–Carathéodory and the Denjoy–Wolff theorems. Two recent accounts...

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...

spherical Bernstein's problem, a generalization of Bernstein's problem Carathéodory conjecture: any convex, closed, and twice-differentiable surface in three-dimensional...

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...

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...

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...

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...

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...

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...

of the Pap test), mathematician Constantin Carathéodory (known for the Carathéodory theorems and Carathéodory conjecture), astronomer E. M. Antoniadi, archaeologists...

available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same temperature...