Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287391514> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4287391514 abstract "The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and sharing a number of fundamental properties with smooth functions, in particular with respect to composition and nonlinear operations. This is how they are still used in informal calculations in Physics. We introduce a category of generalized functions as smooth set-theoretical maps on (multidimensional) points of a ring of scalars containing infinitesimals and infinities. This category extends Schwartz distributions. The calculus of these generalized functions is closely related to classical analysis, with point values, composition, non-linear operations and the generalization of several classical theorems of calculus. Finally, we extend this category of generalized functions into a Grothendieck topos of sheaves over a concrete site. This topos hence provides a suitable framework for the study of spaces and functions with singularities. In this first paper, we present the basic theory; subsequent ones will be devoted to the resulting theory of ODE and PDE." @default.
- W4287391514 created "2022-07-25" @default.
- W4287391514 creator A5054966635 @default.
- W4287391514 creator A5067595490 @default.
- W4287391514 creator A5091121013 @default.
- W4287391514 date "2021-01-12" @default.
- W4287391514 modified "2023-09-26" @default.
- W4287391514 title "A Grothendieck topos of generalized functions I: basic theory" @default.
- W4287391514 doi "https://doi.org/10.48550/arxiv.2101.04492" @default.
- W4287391514 hasPublicationYear "2021" @default.
- W4287391514 type Work @default.
- W4287391514 citedByCount "0" @default.
- W4287391514 crossrefType "posted-content" @default.
- W4287391514 hasAuthorship W4287391514A5054966635 @default.
- W4287391514 hasAuthorship W4287391514A5067595490 @default.
- W4287391514 hasAuthorship W4287391514A5091121013 @default.
- W4287391514 hasBestOaLocation W42873915141 @default.
- W4287391514 hasConcept C124952713 @default.
- W4287391514 hasConcept C134306372 @default.
- W4287391514 hasConcept C136119220 @default.
- W4287391514 hasConcept C142362112 @default.
- W4287391514 hasConcept C177148314 @default.
- W4287391514 hasConcept C182141236 @default.
- W4287391514 hasConcept C199343813 @default.
- W4287391514 hasConcept C202444582 @default.
- W4287391514 hasConcept C2777686260 @default.
- W4287391514 hasConcept C33923547 @default.
- W4287391514 hasConcept C54884031 @default.
- W4287391514 hasConcept C69151251 @default.
- W4287391514 hasConcept C71924100 @default.
- W4287391514 hasConcept C91229774 @default.
- W4287391514 hasConceptScore W4287391514C124952713 @default.
- W4287391514 hasConceptScore W4287391514C134306372 @default.
- W4287391514 hasConceptScore W4287391514C136119220 @default.
- W4287391514 hasConceptScore W4287391514C142362112 @default.
- W4287391514 hasConceptScore W4287391514C177148314 @default.
- W4287391514 hasConceptScore W4287391514C182141236 @default.
- W4287391514 hasConceptScore W4287391514C199343813 @default.
- W4287391514 hasConceptScore W4287391514C202444582 @default.
- W4287391514 hasConceptScore W4287391514C2777686260 @default.
- W4287391514 hasConceptScore W4287391514C33923547 @default.
- W4287391514 hasConceptScore W4287391514C54884031 @default.
- W4287391514 hasConceptScore W4287391514C69151251 @default.
- W4287391514 hasConceptScore W4287391514C71924100 @default.
- W4287391514 hasConceptScore W4287391514C91229774 @default.
- W4287391514 hasLocation W42873915141 @default.
- W4287391514 hasOpenAccess W4287391514 @default.
- W4287391514 hasPrimaryLocation W42873915141 @default.
- W4287391514 hasRelatedWork W2028522012 @default.
- W4287391514 hasRelatedWork W2075513489 @default.
- W4287391514 hasRelatedWork W2165986557 @default.
- W4287391514 hasRelatedWork W2315835747 @default.
- W4287391514 hasRelatedWork W2976300594 @default.
- W4287391514 hasRelatedWork W3134839630 @default.
- W4287391514 hasRelatedWork W3183298406 @default.
- W4287391514 hasRelatedWork W4287391514 @default.
- W4287391514 hasRelatedWork W4312106945 @default.
- W4287391514 hasRelatedWork W73582086 @default.
- W4287391514 isParatext "false" @default.
- W4287391514 isRetracted "false" @default.
- W4287391514 workType "article" @default.