Constructive decomposition of any \(L^1(a, b)\) function as sum of a strongly convergent series of integrable functions each one positive or negative exactly in open sets
DOI10.1007/s00009-023-02414-1zbMath1524.26018OpenAlexW4378471040MaRDI QIDQ6159754
António Ornelas, Clara Carlota
Publication date: 20 June 2023
Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00009-023-02414-1
Sobolev functionscap functions and cup functionslocally monotone absolutely continuous functionspositivity sets and negativity sets of a Lebesgue integrable function
Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Monotonic functions, generalizations (26A48) Absolutely continuous real functions in one variable (26A46)
Cites Work
- The DuBois-Reymond differential inclusion for autonomous optimal control problems with pointwise-constrained derivatives
- Existence of scalar minimizers for nonconvex simple integrals of sum type
- Existence of vector minimizers for nonconvex 1-dim integrals with almost convex Lagrangian
- Strong convergence results related to strict convexity
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