Algebrability and nowhere Gevrey differentiability

DOI10.1007/s11856-014-1104-1zbMath1331.46020OpenAlexW2035902256MaRDI QIDQ2339728

J. Alberto Conejero, Françoise Bastin, Céline Esser, Juan B. Seoane-Sepúlveda

Publication date: 2 April 2015

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10251/64755

zbMATH Keywords

algebrabilitylineabilityGevrey differentiable functionnowhere Gevrey differentiability

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Vector spaces, linear dependence, rank, lineability (15A03) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items

Algebraic genericity and special properties within sequence spaces and series ⋮ On inequalities for convex functions ⋮ Cardinal coefficients related to surjectivity, Darboux, and Sierpiński-Zygmund maps ⋮ Large algebras of singular functions vanishing on prescribed sets ⋮ Modes of convergence in nets, counterexamples, and lineability ⋮ Self-similar functions, fractals and algebraic genericity ⋮ Peano curves on topological vector spaces ⋮ Lineability, algebrability, and sequences of random variables ⋮ Highly tempering infinite matrices. II: From divergence to convergence via Toeplitz-Silverman matrices ⋮ Basic sequences and spaceability in \(\ell_p\) spaces ⋮ Lineability criteria, with applications ⋮ Unnamed Item ⋮ Lineability, differentiable functions and special derivatives ⋮ Algebraic genericity and summability within the non-Archimedean setting ⋮ Nowhere Hölderian functions and Pringsheim singular functions in the disc algebra ⋮ Algebras of measurable extendable functions of maximal cardinality ⋮ On functions that are almost continuous and perfectly everywhere surjective but not Jones. Lineability and additivity ⋮ Large function algebras with certain topological properties ⋮ Generic results in classes of ultradifferentiable functions ⋮ Convolution functions that are nowhere differentiable ⋮ \([\mathcal{S}\)-linear and convex structures in function families] ⋮ Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces ⋮ Discontinuous, although ``highly differentiable, real functions and algebraic genericity ⋮ Banach spaces and Banach lattices of singular functions ⋮ Classical vs. non-Archimedean analysis: an approach via algebraic genericity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximal spaceability in sequence spaces
• On lineability of sets of continuous functions
• Lineability, spaceability, and algebrability of certain subsets of function spaces
• On dense-lineability of sets of functions on \(\mathbb R\)
• Algebras in sets of queer functions
• Nonseparable spaceability and strong algebrability of sets of continuous singular functions
• Additivity and lineability in vector spaces
• Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
• Lineability of sets of nowhere analytic functions
• A new higher order chain rule and Gevrey class
• Linear subsets of nonlinear sets in topological vector spaces
• Prevalence of ``nowhere analyticity
• ON VERY NON-LINEAR SUBSETS OF CONTINUOUS FUNCTIONS
• Algebraic genericity of strict-order integrability
• Infinite dimensional Banach spaces of functions with nonlinear properties
• Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
• Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions
• Lineability and spaceability of sets of functions on $\mathbb {R}$
• There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable
• Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions
• Strong algebrability of sets of sequences and functions
• Distinguished subspaces of L_pof maximal dimension
• Some results and open questions on spaceability in function spaces
• When the Identity Theorem “Seems” to Fail
• Algebrability of the set of non-convergent Fourier series
• Unendlich oft differenzierbare nicht‐analytische Funktionen

This page was built for publication: Algebrability and nowhere Gevrey differentiability