• 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)...
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  • Thumbnail for Riemann mapping theorem
    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
  • 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
  • Thumbnail for Dirac delta function
    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
  • Thumbnail for Krein–Milman theorem
    Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex...
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  • "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
  • _{m}{\overline {\lambda _{n}}}=2(1-|z|^{2})\,\Re \,f(z).} Bochner's theorem Carathéodory, C. (1907), "Über den Variabilitätsbereich der Koeffizienten von...
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  • 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...
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  • sense of the Carathéodory kernel theorem. If D {\displaystyle D} denotes the unit disk in C {\displaystyle \mathbb {C} } , this theorem implies that the...
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  • Thumbnail for David Hilbert
    Hilbert–Burch theorem Hilbert's irreducibility theorem Hilbert's Nullstellensatz Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Hilbert's...
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  • 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
  • Thumbnail for Mikhael Gromov (mathematician)
    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...
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  • 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...
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  • In nonlinear programming there are several multiplier rules, e.g. the Carathéodory–John Multiplier Rule and the Convex Multiplier Rule, for inequality constraints...
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  • Thumbnail for Lipót Fejér
    Fourier series. Fejér collaborated to produce important papers, one with Carathéodory on entire functions in 1907 and another major work with Frigyes Riesz...
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  • 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
  • Thumbnail for Donald Sarason
    Using reproducing kernel Hilbert space techniques, he gave elegant proofs of the Julia–Carathéodory and the Denjoy–Wolff theorems. Two recent accounts...
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  • Thumbnail for Harmonic measure
    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...
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  • 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...
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    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...
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  • 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...
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  • 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...
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  • Thumbnail for Subbaramiah Minakshisundaram
    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...
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    of the Pap test), mathematician Constantin Carathéodory (known for the Carathéodory theorems and Carathéodory conjecture), astronomer E. M. Antoniadi, archaeologists...
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  • Thumbnail for Thermodynamic temperature
    available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same temperature...
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