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Differentiable, Nowhere Analytic Functions
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This article is published in American Mathematical Monthly.The article was published on 1984-12-01. It has received 20 citations till now. The article focuses on the topics: Analytic function & Differentiable function.read more
Citations
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Linear subsets of nonlinear sets in topological vector spaces
TL;DR: The lineability and spaceability of algebraic structures has been studied extensively in real and complex analysis, operator theory, summability theory, polynomials in Banach spaces, hypercyclicity and chaos, and general functional analysis as mentioned in this paper.
Journal ArticleDOI
Lineability criteria, with applications
TL;DR: In this paper, several lineability criteria are provided and applied to specific topological vector spaces, mainly function spaces, including hypercyclic vectors, holomorphic mappings, Riemann non-Lebesgue integrable functions, sequences not satisfying the Lebesgue dominated convergence theorem, nowhere analytic functions, bounded variation functions, entire functions with fast growth and Peano curves, among others, are analyzed from the point of view of lineability.
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Lineability criteria, with applications
TL;DR: In this paper, several lineability criteria are provided and applied to specific topological vector spaces, mainly function spaces, including hypercyclic vectors, holomorphic mappings, Riemann non-Lebesgue integrable functions, sequences not satisfying the Lebesgue dominated convergence theorem, nowhere analytic functions, bounded variation functions, entire functions with fast growth and Peano curves, among others, are analyzed from the point of view of lineability.
Journal ArticleDOI
Lineability of sets of nowhere analytic functions
TL;DR: In this article, it was shown that the space of real C∞-smooth functions on (0, 1) does contain a dense linear submanifold, except for zero.
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Analyticity results in Bernoulli percolation
TL;DR: In this paper, it was shown that the susceptibility is analytic in the subcritical interval for all transitive short- or long-range models, and that p bond c < 1/2 for certain families of triangulations for which Benjamini & Schramm conjectured that p site c ≤ 1/ 2.
References
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Book
The theory of functions
TL;DR: Alfaro et al. as mentioned in this paper conservado en la Biblioteca del Campus de Mostoles de la Universidad Rey Juan Carlos (sign. 517.5 TIT THE).
Book
Real and abstract analysis
Edwin Hewitt,Karl R. Stromberg +1 more
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.
Journal ArticleDOI
Real and Abstract Analysis. By E. Hewitt and K. Stromberg Pp. viii, 476. 1965. (Springer-Verlag.)
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Most infinitely differentiable functions are nowhere analytic
TL;DR: In this article, a natural metric, d, on the space of infinitely differentiable real valued functions defined on an open subset U of the real numbers, R, is defined, and the elements of C∞, which are analytic near at least one point of U comprise a first category subset of C ∞,.