Analytic Extensions of Differentiable Functions Defined in Closed Sets
From MaRDI portal
Publication:4755397
DOI10.2307/1989708zbMath0008.24902OpenAlexW4255596505MaRDI QIDQ4755397
Publication date: 1934
Full work available at URL: https://doi.org/10.2307/1989708
Related Items
A -seeley-extension-theorem for Bastiani’s differential calculus, Nirenberg’s contributions to linear partial differential equations: Pseudo-differential operators and solvability, Linéarisation des perturbations holomorphes des rotations et applications, On the Existence of Functions Having Given Partial Derivatives on a Curve, On the theory of divergence-measure fields and its applications, Stiefel—Whitney classes for coherent real analytic sheaves, Metrics and convergence in moduli spaces of maps, Intrinsic Characterizations of Tangent Spaces, A tour of the theory of absolutely minimizing functions, Functions not Constant on Fractal Quasi-Arcs of Critical Points, On the algebra of functions 𝒞^{𝓀}-extendable for each 𝓀 finite, Unnamed Item, Variational problems within the class of solutions of a partial differential equation, A Tour on p(x)-Laplacian Problems When p = ∞, A C^k Lusin approximation theorem for real-valued functions on Carnot groups, Intégrales orbitales sur les groupes de Lie réductifs, \(C^2\) interpolation with range restriction, Dependency of the positive and negative long-time behaviors of flows on surfaces, Compact Hölder retractions and nearest point maps, Rigidity and flexibility of isometric extensions, Inframonogenic decomposition of higher‐order Lipschitz functions, Complexities of differentiable dynamical systems, Symmetry results for Serrin-type problems in doubly connected domains, On the projective description of spaces of ultradifferentiable functions of Roumieu type, On the Critical Degree of Differentiability of a Complex Planar Curve, Finely continuously differentiable functions, Doubling coverings via resolution of singularities and preparation, Unnamed Item, Variational Problems within the Class of Solutions of a Partial Differential Equation, Unnamed Item, A Note on the Convergence of Alternating Direction Methods, The trace of jet space 𝐽^{𝑘}Λ^{𝜔} to an arbitrary closed subset of ℝⁿ, Generalized Hestenes’ Lemma and extension of functions, On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate, Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds, Differentiable Structures on Function Spaces, Formulas to represent functions by their derivatives, A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions, Unnamed Item, Unnamed Item, Formulas to represent functions by their derivatives, Whitney’s example by way of Assouad’s embedding, On the total disconnectedness of the quotient Aubry set, Différentiabilité fine et différentiabilité sur des compacts, Structure and \(f\)-dependence of the a.c.i.m. for a unimodal map \(f\) of Misiurewicz type, From formal numerical solutions of elliptic PDE's to the true ones, Unnamed Item, Unnamed Item, Packing smooth curves inRq, Decay rates of oscillatory integral operators in “1 + 2” dimensions, Unnamed Item, Non-unicité pour des opérateurs différentiels à caractéristiques complexes simples, Packing smooth curves inRq, Surjectivity of Euler type differential operators on spaces of smooth functions, Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo), Unnamed Item, Analytic Extension of Non Quasi - Analytic Whitney Jets of Beurling Type, Différentiabilité fine et capacités, Approximation et interpolation des fonctions différentiables de plusieurs variables, Zur Potentialtheorie für stark elliptische Systeme mit konstanten Koeffizienten Dem 25. Jahrestag der DDR gewidmet, Representing a Differentiable Function as a Cartesian Product, From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems, Differentiable functions, Wiener measures and some questions of approximation in Banach spaces, Atomic cluster expansion: completeness, efficiency and stability, Finiteness principles for smooth selection, Mixed type, nonlinear systems in polygonal domains, Differentiable Restrictions of Real Functions, Explicit formulas for 𝐶^{1,1} Glaeser-Whitney extensions of 1-Taylor fields in Hilbert spaces, Chain recurrence, semiflows, and gradients, Surjective Mappings Whose Differential is Nowhere Surjective, Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem, The topological structure of the set of stable solutions of a differential system, On the division of distributions by polynomials, A non uniqueness result for operators of principal type, Problems of representation and uniqueness for functions of a complex variable, O-minimal version of Whitney's extension theorem, Minimal Lipschitz extensions to differentiable functions defined on a Hilbert space, The geometry of Whitney's critical sets, Cauchy integral operators involving higher order Lipschitz classes in the poly-analytic function theory, Yang-Mills moduli spaces over an orientable closed surface via Fréchet reduction, Unnamed Item, A nonlinear Korn inequality on a surface with an explicit estimate of the constant, Whitney extension operators with arbitrary loss of differentiability, Extension operators for smooth functions on compact subsets of the reals, On Burenkov's extension operator preserving Sobolev-Morrey spaces on Lipschitz domains, Necessary and sufficient condition for global controllability of a class of affine nonlinear systems, Extension procedures for lattice Lipschitz operators on Euclidean spaces, Existence of invariant curves with prescribed frequency for degenerate area preserving mappings, On the empirical estimation of integral probability metrics, On the regularity of non-scattering anisotropic inhomogeneities, Nonnegative \(\mathrm C^2(\mathbb R^2)\) interpolation, \(C^2(\mathbb{R}^2)\) nonnegative extension by bounded-depth operators, Whitney’s extension problem for multivariate 𝐶^{1,𝜔}-functions, The Whitney extension problem and Lipschitz selections of set-valued mappings in jet-spaces, Whitney's extension theorem in o-minimal structures, Topologie de certains espaces de plongements, An explicit solution of the Lipschitz extension problem, Multiplicateurs rugueux des fonctions différentiables et synthèse spectrale, On global controllability of affine nonlinear systems with a triangular-like structure, The Whitney extension theorem for \(C^1\), horizontal curves in the Heisenberg group, \(C^1\) extensions of functions and stabilization of Glaeser refinements, Markov inequality in several variables, Concentration inequalities for polynomials of contracting Ising models, On a hydrogen atom, Uniqueness for elliptic operators on with unbounded coefficients, A coordinate-free proof of the finiteness principle for Whitney's extension problem, Extension criteria for homogeneous Sobolev spaces of functions of one variable, Persistence of the non-twist torus in nearly integrable hamiltonian systems, The concept of integrability on cantor sets for Hamiltonian systems, Metric spaces and ideals of functions, An extension theorem for conformal gauge singularities, A conformal extension theorem based on null conformal geodesics, McShane-Whitney pairs, Convexity Conditions and Intersections with Smooth Functions, Axioms for Euclidean Green's functions, C\(^k\) approximation by holomorphic functions and \(\bar \partial\)-closed forms on C\(^k\) submanifolds of a complex manifold, On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik boundary point principle, A Serrin-type problem with partial knowledge of the domain, Existence of invariant tori in reversible mappings, Nonlinear partial differential equations of fourth order under mixed boundary conditions, Some regularity results for Lorentz-Finsler spaces, Dual of the function algebra 𝐴^{-∞}(𝐷) and representation of functions in Dirichlet series, Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces, Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions, Universality and ultradifferentiable functions: Fekete’s theorem, On properties of geometric preduals of \({\mathrm C^{k,\omega}}\) spaces, Hairer's reconstruction theorem without regularity structures, Hyperbolic unfoldings of minimal hypersurfaces, A density result on Orlicz-Sobolev spaces in the plane, Stable manifolds to bounded solutions in possibly ill-posed PDEs, Whitney’s extension problems and interpolation of data, Lipschitz approximation on closed sets, Tug-of-war and the infinity Laplacian, Potentialtheoretische Betrachtungen bei der Bipotentialgleichung, Differenzierbare Strukturen auf Mannigfaltigkeiten ohne abzählbare Basis, Entire functions mapping uncountable dense sets of reals onto each other monotonically, Extension of functions satisfying Lipschitz conditions, The Stone-Weierstrass theorem in Lipschitz algebras, The Stone-Weierstrass theorem in certain Banach algebras of Fourier type, Gauss images of hyperbolic cusps with convex polyhedral boundary, Analytic extension of smooth functions, Sufficient parameters: Solution of the minimal dimensionality problem, The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves, On the continuous dependence of \(C^ r\) solutions of a functional equation on the given functions, Peano differentiable extensions in o-minimal structures, Homoclinic points in conservative systems, On certain linear operators in spaces of ultradifferentiable functions, Deformations of metrics and associated harmonic maps, Traces of $C^{k}$ functions on weak Markov subsets of $\mathbb R^{n}$, Persistence of Floquet invariant tori for a class of non-conservative dynamical systems, A general conformal geometric reflection principle, Extension of smooth functions from finitely connected planar domains, Differentiating the absolutely continuous invariant measure of an interval map \(f\) with respect to \(f\), A stochastic approximation scheme and convergence theorem for particle interactions with perfectly reflecting boundary conditions, Localization for multiple Fourier series with ``\(J_k\)-lacunary sequence of partial sums in Orlicz classes, Dirichlet and Neumann problems for planar domains with parameter, Pointwise characterization of Sobolev classes, Sobolev extension by linear operators, A new definition of rough paths on manifolds, An introduction to differential geometry with applications to elasticity, Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones, Extension of ultradifferentiable functions, Dyadic Hermite interpolants on a triangulation, Limit problems for a fractional \(p\)-Laplacian as \(p\to\infty\), General KAM theorems and their applications to invariant tori with prescribed frequencies, A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems, Representation theorem for locally defined operators in the space of Whitney differentiable functions, Adaptive Bayesian estimation using a Gaussian random field with inverse gamma bandwidth, Smoothness of the density of states in the Anderson model on a one- dimensional strip, On a generalization of Nikolskij's extension theorem in the case of two variables., Ballistic motion in one-dimensional quasi-periodic discrete Schrödinger equation, Analytic extension of non quasi-analytic Whitney jets of Roumieu type, A priori estimate of gradient of a solution of a certain differential inequality and quasiconformal mappings, On elliptic lower dimensional tori in Hamiltonian systems, Resummation of perturbation series and reducibility for Bryuno skew-product flows, A bounded linear extension operator for \(L^{2,p}(\mathbb R^2)\), Pre-dual of the function algebra \(A^{-\infty}(D)\) and representation of functions in Dirichlet series, Isotropic hypersurfaces and minimal extensions of Lipschitz functions, Schoenflies extensions of analytic families of diffeomorphisms, Analytic diffcomorphisms approximating \(C^ m\)-diffeomorphisms, On invariant tori of nearly integrable Hamiltonian systems with quasiperiodic perturbation, The completeness of Maxwell's stress function representation, Calculation of the bidual for some function spaces. Integrable distributions, Stability of some states of plane deformation, The \(C^m\) norm of a function with prescribed jets. I., Approximation by polyhedral \(G\) chains in Banach spaces, On invariant sets in Lagrangian graphs, Equivalent norms in Sobolev spaces and norm of extension operators, Ein Kriterium für die Approximierbarkeit von Funktionen aus Sobolewschen Räumen durch glatte Funktionen, Uniqueness of SRB measures for transitive diffeomorphisms on surfaces, On equivalence of ideals of real global analytic functions and the 17th Hilbert problem, Holomorphic extensions of Whitney jets, Interpolating and orthogonal polynomials on fractals, On the reducibility for a class of quasi-periodic Hamiltonian systems with small perturbation parameter, Quasi-periodic solutions for two-level systems, Quasiconformal mappings and extendability of functions in Sobolev spaces, Relations among Whitney sets, self-similar arcs and quasi-arcs, Holomorphic convexity and Carleman approximation by entire functions on Stein manifolds, Extension operators with analytic values, Generalized localization and convergence tests for double trigonometric Fourier series of functions from \(L_ p\), \(p>1\), \((K, K^{\prime})\)-quasiconformal harmonic mappings, A linear extension operator for Whitney fields on closed o-minimal sets, Local inverses of shift maps along orbits of flows, Pointwise regularity of the free boundary for the parabolic obstacle problem, To the theory of the Dirichlet and Neumann problems for strongly elliptic systems in Lipschitz domains, Taylorian fields and subdivision algorithms, Integrable boundaries and fractals for Hölder classes; the Gauss-Green theorem, Solution operators for the \(\bar\partial\)-equation on non-transversal intersections of strictly pseudoconvex domains, On the average period of an elliptic curve, Ballistic transport and absolute continuity of one-frequency Schrödinger operators, Differentiable McCormick relaxations, A KAM theorem for a class of nearly integrable symplectic mappings, On the \(\phi \)-hyperderivative of the \(\psi \)-Cauchy-type integral in Clifford analysis, Recovery of immersions from their metric tensors and nonlinear Korn inequalities: a brief survey, On Whitney's extension theorem for ultradifferentiable functions, Smooth extensions of functions on separable Banach spaces, Tame linear extension operators for smooth Whitney functions, Taylor formula on step two Carnot groups, Axioms for Euclidean Green's functions. II, A dual characterization of the \(\mathcal C^1\) harmonic capacity and applications, On superpositions of continuous functions, The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients, Non-existence of a continuum that models a Newtonian system of interacting particles, Die Gute der \(L_p\)-Approximation durch Kantorovic-Polynome, Complexes of differential operators. The Mayer-Vietoris sequence, Extensions of Lipschitz maps into Banach spaces, Anisotropic smoothness classes: from finite element approximation to image models, Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. I, An example related to Whitney extension with almost minimal \(C^m\) norm, Quelques théorème de décomposition des ultradistributions, On the convergence of double Fourier series of functions from \(L_p\), \(p>1\), On the differentiability of functions, The Hadamard variational formula for the Green functions of some normal elliptic boundary value problems, Extension of Whitney fields from subanalytic sets, Fortsetzungen von \(C^\infty\)-Funktionen, welche auf einer abgeschlossenen Menge in \(R^ n\) definiert sind, Existence of \(p\) harmonic multiple valued maps into a separable Hilbert space, Line bundle convexity of pseudoconvex domains in complex manifolds, Extension of \(C^{m, \omega}\)-smooth functions by linear operators, Fitting a \(C^m\)-smooth function to data. II, The \(C^m\) norm of a function with prescribed jets. II, Extending smooth functions from linear subspaces of locally convex spaces, Existence of invariant tori for certain weakly reversible mappings, Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary, Teleman localization of Hochschild homology in a singular setting, Étude de quelques algèbres tayloriennes, KAM tori for higher dimensional beam equation with a fixed constant potential, The Whitney problem of existence of a linear extension operator, Differentiability properties of isotropic functions, On finite \(C^ k \)left determinacy, Equivalence of differentiable mappings and analytic mappings, Unicité et non unicité du problème de Cauchy pour une classe d'opérateurs différentiels à caractéristiques doubles, An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\), Quantitative Whitney-type theorems, Real analytic SL(n,\({\mathbb{R}})\) actions on spheres, Differentiability properties of symmetric and isotropic functions, Piecewise linearization of real analytic functions, Orbital integrals on reductive Lie algebras, Examples of compact sets with non-empty interior which do not admit a continuous linear extension operator for ultradifferentiable functions of Beurling type, Smooth positive extensions and nonlinear programming
