Lineability
-10%
portes grátis
Lineability
The Search for Linearity in Mathematics
Aron, Richard M.; Pellegrino, Daniel M.; Bernal-Gonzalez, Luis; Sepulveda, Juan B. Seoane
Taylor & Francis Ltd
02/2018
Mole
Inglês
9781138894433
15 a 20 dias
Descrição não disponível.
Preliminary Notions and Tools Cardinal numbers Cardinal arithmetic Basic concepts and results of abstract and linear algebra Residual subsets Lineability, spaceability, algebrability, and their variants Real Analysis What one needs to know Weierstrass' monsters Differentiable nowhere monotone functions Nowhere analytic functions and annulling functions Surjections, Darboux functions, and related properties Other properties related to the lack of continuity Continuous functions that attain their maximum at only one point Peano maps and space-filling curves Complex Analysis What one needs to know Nonextendable holomorphic functions: genericity Vector spaces of nonextendable functions Nonextendability in the unit disc Tamed entire functions Wild behavior near the boundary Nowhere Gevrey differentiability Sequence Spaces, Measure Theory, and Integration What one needs to know Lineability and spaceability in sequence spaces Non-contractive maps and spaceability in sequence spaces Lineability and spaceability in Lp[0, 1] Spaceability in Lebesgue spaces Lineability in sets of norm attaining operators in sequence spaces Riemann and Lebesgue integrable functions and spaceability Universality, Hypercyclicity, and Chaos What one needs to know Universal elements and hypercyclic vectors Lineability and dense-lineability of families of hypercyclic vectors Wild behavior near the boundary, universal series, and lineability Hypercyclicity and spaceability Algebras of hypercyclic vectors Supercyclicity and lineability Frequent hypercyclicity and lineability Distributional chaos and lineability Zeros of Polynomials in Banach Spaces What one needs to know Zeros of polynomials: the results Miscellaneous Series in classical Banach spaces Dirichlet series Non-convergent Fourier series Norm-attaining functionals Annulling functions and sequences with finitely many zeros Sierpinski-Zygmund functions Non-Lipschitz functions with bounded gradient The Denjoy-Clarkson property General Techniques What one needs to know The negative side When lineability implies dense-lineability General results about spaceability An algebrability criterion Additivity and cardinal invariants: a brief account Bibliography Index Exercises, Notes, and Remarks appear at the end of each chapter.
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Preliminary Notions and Tools Cardinal numbers Cardinal arithmetic Basic concepts and results of abstract and linear algebra Residual subsets Lineability, spaceability, algebrability, and their variants Real Analysis What one needs to know Weierstrass' monsters Differentiable nowhere monotone functions Nowhere analytic functions and annulling functions Surjections, Darboux functions, and related properties Other properties related to the lack of continuity Continuous functions that attain their maximum at only one point Peano maps and space-filling curves Complex Analysis What one needs to know Nonextendable holomorphic functions: genericity Vector spaces of nonextendable functions Nonextendability in the unit disc Tamed entire functions Wild behavior near the boundary Nowhere Gevrey differentiability Sequence Spaces, Measure Theory, and Integration What one needs to know Lineability and spaceability in sequence spaces Non-contractive maps and spaceability in sequence spaces Lineability and spaceability in Lp[0, 1] Spaceability in Lebesgue spaces Lineability in sets of norm attaining operators in sequence spaces Riemann and Lebesgue integrable functions and spaceability Universality, Hypercyclicity, and Chaos What one needs to know Universal elements and hypercyclic vectors Lineability and dense-lineability of families of hypercyclic vectors Wild behavior near the boundary, universal series, and lineability Hypercyclicity and spaceability Algebras of hypercyclic vectors Supercyclicity and lineability Frequent hypercyclicity and lineability Distributional chaos and lineability Zeros of Polynomials in Banach Spaces What one needs to know Zeros of polynomials: the results Miscellaneous Series in classical Banach spaces Dirichlet series Non-convergent Fourier series Norm-attaining functionals Annulling functions and sequences with finitely many zeros Sierpinski-Zygmund functions Non-Lipschitz functions with bounded gradient The Denjoy-Clarkson property General Techniques What one needs to know The negative side When lineability implies dense-lineability General results about spaceability An algebrability criterion Additivity and cardinal invariants: a brief account Bibliography Index Exercises, Notes, and Remarks appear at the end of each chapter.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
