A Convenient Notion of Compact Set for Generalized Functions

DOI10.1017/S0013091516000559zbMath1400.46036arXiv1411.7292OpenAlexW2963627179MaRDI QIDQ4608140

Michael Kunzinger, Paolo Giordano

Publication date: 16 March 2018

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7292

zbMATH Keywords

Colombeau generalized functionsgeneralized smooth functionslocally convex modulesfunctionally compact sets

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Topological rings and modules (13J99) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (9)

New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem ⋮ The classical theory of calculus of variations for generalized functions ⋮ Categorical frameworks for generalized functions ⋮ Hyper-power series and generalized real analytic functions ⋮ Inverse Function Theorems for Generalized Smooth Functions ⋮ An Application of Internal Objects to Microlocal Analysis in Generalized Function Algebras ⋮ Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers ⋮ Calculus of variations and optimal control for generalized functions ⋮ Hyperseries in the non-Archimedean ring of Colombeau generalized numbers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strongly internal sets and generalized smooth functions
• Nonstandard principles for generalized functions
• Categorical frameworks for generalized functions
• Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory
• Natural topologies on Colombeau algebras
• A nonlinear theory of generalized functions.
• A discontinuous Colombeau differential calculus
• New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem
• Differential calculus and integration of generalized functions over membranes
• Internal sets and internal functions in Colombeau theory
• Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory
• Topological structures in Colombeau algebras: Investigation of the duals of \(\mathcal G_c(\Omega)\), \(\mathcal G(\Omega)\) and \(\mathcal G_{\mathcal S}(\mathbb R^n)\)
• SOME STRUCTURAL PROPERTIES OF THE TOPOLOGICAL RING OF COLOMBEAU'S GENERALIZED NUMBERS
• Asymptotic gauges: Generalization of Colombeau type algebras
• Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems
• Unifying order structures for Colombeau algebras
• Closed graph and open mapping theorems for topological $ \tilde \lc $-modules and applications
• On Lorentz geometry in algebras of generalized functions
• Algebraic and Geometric Theory of the Topological Ring of Colombeau Generalized Functions
• Ideals in the Ring of Colombeau Generalized Numbers
• Some remarks on functoriality of Colombeau's construction; topological and microlocal aspects and applications
• Characterization of colombeau generalized functions by their pointvalues
• Locally convex topological algebras of generalized functions: Compactness and nuclearity in a nonlinear context
• Sequence spaces with exponent weights. Realizations of Colombeau type algebras
• On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

This page was built for publication: A Convenient Notion of Compact Set for Generalized Functions