mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after French mathematician Paul Montel, and...

theory of ordinary differential equations, Montel's theorem in complex analysis, and the Peter–Weyl theorem in harmonic analysis and various results concerning...

a Montel space, named after Paul Montel, is any topological vector space (TVS) in which an analog of Montel's theorem holds. Specifically, a Montel space...

and f ′ ( a ) > 0 {\displaystyle f'(a)>0} . It is a normal family by Montel's theorem. By the characterization of simple-connectivity, for b ∈ C ∖ G {\displaystyle...

analysis) Monodromy theorem (complex analysis) Montel's theorem (complex analysis) Morera's theorem (complex analysis) Nachbin's theorem(complex analysis)...

components that are not eventually periodic. No-wandering-domain theorem Montel's theorem John Domains Basins of attraction wikibooks : parabolic Julia sets...

analysis. Montel was a student of Émile Borel at the Sorbonne. Henri Cartan, Jean Dieudonné and Miron Nicolescu were among his students. Montel's most important...

analytic functions. It is another name for the stronger version of Montel's theorem. Let F {\displaystyle {\mathcal {F}}} be a family of analytic functions...

f^{n_{k}}} , convergent in the same sense to g, say. Such limits exist by Montel's theorem, and if g is non-constant, it can also be assumed that f n k + 1 −...

polynomials Laplace–Stieltjes transform Lebesgue–Stieltjes integral Montel's theorem Riemann–Stieltjes integral Stieltjes constants Stieltjes matrix Stieltjes...

family is normal: Montel's theorem states that a family of locally bounded holomorphic functions is normal. The Montel-Caratheodory theorem states that the...

existence can be proved by using a normal family argument involving Montel's theorem. Let dimH denote Hausdorff dimension and H1 denote 1-dimensional Hausdorff...

Method of steepest descent Montel's theorem Periodic points of complex quadratic mappings Pick matrix Runge approximation theorem Schwarz lemma Weierstrass...

open set U, f is univalent on D and f(D) = U. Using Hurwitz's theorem and Montel's theorem, it is straightforward to check that if fn tends uniformly on...

In real analysis, the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S {\displaystyle S} of Euclidean space R n {\displaystyle...

compositions of analytic functions Montel's theorem Poincaré metric Schwarz lemma Riemann mapping theorem Carathéodory's theorem (conformal mapping) Böttcher's...

{\displaystyle f} is continuous. Modes of convergence (annotated index) Montel's theorem Reinhold Remmert Theory of complex functions (1991 Springer) p. 95...

In the mathematical field of complex analysis, the Looman–Menchoff theorem states that a continuous complex-valued function defined in an open set of...

established precise estimates that sharpened the qualitative results of Montel's theorem. He was elected in 1956 a corresponding member and in 1959 a full member...

the Bergman metric, for which the isometries form a Lie group; by Montel's theorem, the group of biholomorphisms is a closed subgroup. That HT is a Lie...

graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the closed graph theorem is...

closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem states that...

developed by Alexander Grothendieck while investigating the Schwartz kernel theorem and published in (Grothendieck 1955). We now describe this motivation....

this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...

Bourbaki–Alaoglu theorem Dual pair F-space Fréchet space Krein–Milman theorem Locally convex topological vector space Mackey topology Mackey–Arens theorem Montel space...

paradox Borel–Cantelli lemma Borel–Carathéodory theorem Heine–Borel theorem Borel determinacy theorem Borel right process Borel set Borel summation Borel...

functional analysis, like the open mapping theorem, the closed graph theorem, and the Banach–Steinhaus theorem, still hold. Recall that a seminorm ‖ ⋅ ‖...

24033/bsmf.1131. JFM 54.0834.01. Fatou conjecture Fatou's theorem Fatou set Fatou–Lebesgue theorem (same as Fatou's lemma) Classification of Fatou components...

compactly supported function, and the Titchmarsh convolution theorem Hörmander (1983, Theorem 4.3.3) implies that: ch ⁡ ( supp ⁡ ( f ∗ T ) ) = ch ⁡ ( supp...

Theorem V.4.2, p. 135. Since weak compactness and weak sequential compactness coincide by the Eberlein–Šmulian theorem. Diestel 1984, p. 6. Theorem 1...