@article{CTGDC_2006__47_1_2_0, author = {Kock, Anders and Reyes, Gonzalo}, title = {Distributions and heat equation in $SDG$}, journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, pages = {2--28}, publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS}, volume = {47}, number = {1}, year = {2006}, mrnumber = {2220059}, zbl = {1098.58002}, language = {en}, url = {http://www.numdam.org/item/CTGDC_2006__47_1_2_0/} }
TY - JOUR AU - Kock, Anders AU - Reyes, Gonzalo TI - Distributions and heat equation in $SDG$ JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques PY - 2006 SP - 2 EP - 28 VL - 47 IS - 1 PB - Dunod éditeur, publié avec le concours du CNRS UR - http://www.numdam.org/item/CTGDC_2006__47_1_2_0/ LA - en ID - CTGDC_2006__47_1_2_0 ER -
%0 Journal Article %A Kock, Anders %A Reyes, Gonzalo %T Distributions and heat equation in $SDG$ %J Cahiers de Topologie et Géométrie Différentielle Catégoriques %D 2006 %P 2-28 %V 47 %N 1 %I Dunod éditeur, publié avec le concours du CNRS %U http://www.numdam.org/item/CTGDC_2006__47_1_2_0/ %G en %F CTGDC_2006__47_1_2_0
Kock, Anders; Reyes, Gonzalo. Distributions and heat equation in $SDG$. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 47 (2006) no. 1, pp. 2-28. http://www.numdam.org/item/CTGDC_2006__47_1_2_0/
[1] Théorie des Topos (SGA 4), Springer LNM 269 (1972). | MR
, and ,[2] Iterated integrals of differential forms and loop space homology, Annals of Math. (2) 97 (1972), 217-146. | MR | Zbl
[3] Sur les modèles de la géométrie différentielle synthétique, Cahiers de Topologie et Géometrie Diff. 20 (1979), 231-279. | Numdam | MR | Zbl
,[4] Cartesian Closed Categories and Analysis of Smooth Maps, in "Categories in Continuum Physics", Buffallo 1982 (ed. F.W. Lawvere and S.H. Schanuel), Springer Lecture Notes in Math. 1174 (1986). | MR | Zbl
,[5] Linear Spaces and Differentiation Theory, Wiley 1988. | MR | Zbl
, ,[6] General Topology, Van Nostrand 1955. | MR | Zbl
,[7] Linear Topological Spaces, Van Nostrand 1963. | MR | Zbl
, , and ,[8] Properties of well-adapted models for synthetic differential geometry, Joum. Pure Appl. Alg. 20 (1981), 55-70. | MR | Zbl
[9] Synthetic Differential Geometry, Cambridge University Press 1981. | MR | Zbl
,[10] Calculus of smooth functions between convenient vector spaces, Aarhus Preprint Series 1984/85 No. 18. Retyped in http://home.imf.au.dk/kock/CSF.pdf
,[11] Convenient vector spaces embed into the Cahiers topos, Cahiers de Topologie et Géométrie Diff. Catégoriques 27 (1986), 3-17. | EuDML | Numdam | MR | Zbl
,[12] Models for synthetic integration theory, Math. Scand. 48 (1981), 145-152. | EuDML | MR | Zbl
and ,[13] Corrigendum and addenda to "Convenient vector spaces embed", Cahiers de Topologie et Géométrie Diff. Catégoriques 28 (1987), 99-110. | EuDML | Numdam | MR | Zbl
and ,[14] Some calculus with extensive quantities: wave equation, Theory and Applications of Categories, Vol. 11 (2003), No. 14. | EuDML | MR | Zbl
and ,[15] Convenient Setting of Global Analysis, Amer. Math. Soc. 1997. | MR | Zbl
and ,[16] Basic Concepts of Synthetic Differential Geometry, Kluwer Acad. Publishers 1996. | MR | Zbl
,[17] Catgeories of Space and of Quantity, in "The Space of Mathematics. Philosophical, Epistemological and Historical Explorations", DeGruyter, Berlin 1992, 14-30. | MR | Zbl
,[18] Volterra's Functionals and Covariant Cohesion of Space, Rendiconti del Circolo Mat. di Palermo Serie II, Suppl. 64 (2000), 201-214. | MR | Zbl
,[19] Frechet manifolds as diffeological spaces, Soviet Math. (Iz. vuz) 5 (1992), 36-42. | MR | Zbl
[20] Models for Smooth Infinitesimal Analysis, Springer 1991. | MR | Zbl
and and ,[21] Enriched locally convex structures, Differential Calculus and Riesz representations, Joum. Pure Appl. Alg. 42 (1986), 165-184. | MR | Zbl
,[22] Variétés à bord et topos lisse, in "Analyse dans les topos lisses" (ed. G.E. Reyes), Rapport de Rechercehes D.M.S. 80-12, Université de Montréal 1980.
and ,[23] Théorie des distribution et théorème d'extension de Whitney, in "Analyse dans les topos lisses" (ed. G.E. Reyes), Rapport de Rechercehes D.M.S. 80-12, Université de Montréal 1980.
and[24] A model of SDG in which only trivial distributions with compact support have a density, in http://reyes-reyes.com/gonzalo/recent_work/syntheticdifferential/
,[25] Embedding manifolds with boundary in smooth toposes, in http://reyes-reyes.com/gonzalo/recent_work/syntheticdifferential/ [26]
,[26] Théorie des distributions, Tome 1, Hermann Paris 1957. | MR | Zbl
,[27] Méthodes mathématiques pour les sciences physiques, Hermann Paris 1961. | MR | Zbl
,[28] Extension of C∞ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626. | Zbl
,