Linearity in non-linear problems

By D. Rodríguez, R. Aron, Manuel Maestre. 2001

64 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/90f42b0b0a19c9bd78e3e94bc08dc4f2c1a32c36

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Citations in the corpus

On dense-lineability of sets of functions on R (2009, background): “The terminology of lineable and spaceable was introduced by Gurariy in [1,2] (see [3] as well).”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “32 (Aron, Garćıa, and Maestre, 2000 [19]).”
Algebrability of the set of non-convergent Fourier series (2006, background): “We believe that the terms lineable and spaceable were first introduced in [5] and, later, in [2] and [7] (see also [1]).”
Lineability criteria, with applications (2013, background): “It was mentioned at the beginning of Section 2 that Kierst and Szpilrajn showed the residuality of He(G) (this result was extended by Kahane [67] in 2000 to certain subspaces of H(G)) and that in [5] the dense-lineability and the spaceability ofHe(G) were established (in [85] additional topological ”
Algebras in sets of queer functions (2007, unknown): “Using Taylor’s formula, for a given x 2 [0, 1 ] and for any y 2 [0,1], we may write ( y) := f(y) f(x) as”
Sierpinski-Zygmund functions and other problems on lineability (2010, background): “For every Gδ, density-closed set E, there exists an approximately continuous mapping f0 : R → [0, 1] such that its zero set Zf0 is equal to E.”
Operator ranges and spaceability (2011, background): “) It was highlighted further in [1], where it was pointed out that highly non-linear and apparently pathological sets can often have the property.”
Algebraic genericity of strict-order integrability (2010, background): “In this respect, let us recall some recent terminology introduced in [1], [3], [5] and [8].”