- Aller à la page de la table des matières419
- TABLE DES MATIÈRES NEUVIÈME SÉRIE. - TOME XVIII
- .......... Page(s) .......... 63
- .......... Page(s) .......... 97
- .......... Page(s) .......... 111
- .......... Page(s) .......... 157
- .......... Page(s) .......... 167
- .......... Page(s) .......... 249
- .......... Page(s) .......... 291
- .......... Page(s) .......... 303
- .......... Page(s) .......... 323
- .......... Page(s) .......... 405
- .......... Page(s) .......... 417
- .......... Page(s) .......... 419
- FIN DU TOME XVIII DE LA NEUVIEME SERIE.
- SOMMAIRE DU FASCICULE N° 4
- SOMMAIRE DU FASCICULE N° 3
- SOMMAIRE DU FASCICULE N° 2
ON THE ELEMENTARY SOLUTION. 217
On the elementary solution of the general linear
differential equation of the second order with
analytic coefficients ;
BY T. Y. THOMAS AND E. W. TITT.
Introduction.
Consider the second order differential equation (')
where the g, f and b are analytic functions of the real variables
xl, , xa in a region R of the (real) n-dimensional number space
(n > 2). Or, more generally, owing to its invariance under coor-
dinate transformations, this equation may be considered to be defined
with analytic coefficients g, f and b over an analytic manifold M (2).
We assume that the determinant does not vanish at any point
of the space under consideration.
The following paper is largely, although not entirely, expository.
It is concerned largely with Hadamard's elementary solution of the
equation (A) as treated in Chapter III of his Lectures on Cauchy's
(1) Hereafter the summation convention will be used.
(2) By definition an analytic manifold Oil is a Hausdorff space with coordinate
neighborhoods, homeomorphic to the interior of a spherical surface of n -- I
dimensions in a Euclidean space of n dimensions, and such that the coordinate
relationships between the coordinates of two intersecting neighborhoods are
analytic.
Journ. de Math., tome XVIII. - Fasc. Ill, 1939. 29
On the elementary solution of the general linear
differential equation of the second order with
analytic coefficients ;
BY T. Y. THOMAS AND E. W. TITT.
Introduction.
Consider the second order differential equation (')
where the g, f and b are analytic functions of the real variables
xl, , xa in a region R of the (real) n-dimensional number space
(n > 2). Or, more generally, owing to its invariance under coor-
dinate transformations, this equation may be considered to be defined
with analytic coefficients g, f and b over an analytic manifold M (2).
We assume that the determinant does not vanish at any point
of the space under consideration.
The following paper is largely, although not entirely, expository.
It is concerned largely with Hadamard's elementary solution of the
equation (A) as treated in Chapter III of his Lectures on Cauchy's
(1) Hereafter the summation convention will be used.
(2) By definition an analytic manifold Oil is a Hausdorff space with coordinate
neighborhoods, homeomorphic to the interior of a spherical surface of n -- I
dimensions in a Euclidean space of n dimensions, and such that the coordinate
relationships between the coordinates of two intersecting neighborhoods are
analytic.
Journ. de Math., tome XVIII. - Fasc. Ill, 1939. 29
Le taux de reconnaissance estimé pour ce document est de 98.51%.
En savoir plus sur l'OCR
En savoir plus sur l'OCR
Le texte affiché peut comporter un certain nombre d'erreurs. En effet, le mode texte de ce document a été généré de façon automatique par un programme de reconnaissance optique de caractères (OCR). Le taux de reconnaissance estimé pour ce document est de 98.51%.
- Collections numériques similaires Collections de l’École nationale des ponts et chaussées Collections de l’École nationale des ponts et chaussées /services/engine/search/sru?operation=searchRetrieve&version=1.2&maximumRecords=50&collapsing=true&exactSearch=true&query=colnum adj "EnPC000"
- Auteurs similaires Liouville Joseph Liouville Joseph /services/engine/search/sru?operation=searchRetrieve&version=1.2&maximumRecords=50&collapsing=true&exactSearch=true&query=(dc.creator adj "Liouville Joseph" or dc.contributor adj "Liouville Joseph")Résal Amé Henri Résal Amé Henri /services/engine/search/sru?operation=searchRetrieve&version=1.2&maximumRecords=50&collapsing=true&exactSearch=true&query=(dc.creator adj "Résal Amé Henri" or dc.contributor adj "Résal Amé Henri") Picard Émile Picard Émile /services/engine/search/sru?operation=searchRetrieve&version=1.2&maximumRecords=50&collapsing=true&exactSearch=true&query=(dc.creator adj "Picard Émile" or dc.contributor adj "Picard Émile") Jordan Camille Jordan Camille /services/engine/search/sru?operation=searchRetrieve&version=1.2&maximumRecords=50&collapsing=true&exactSearch=true&query=(dc.creator adj "Jordan Camille" or dc.contributor adj "Jordan Camille")
-
-
Page
chiffre de pagination vue 229/450
- Recherche dans le document Recherche dans le document https://gallica.bnf.fr/services/ajax/action/search/ark:/12148/bpt6k6451939t/f229.image ×
Recherche dans le document
- Partage et envoi par courriel Partage et envoi par courriel https://gallica.bnf.fr/services/ajax/action/share/ark:/12148/bpt6k6451939t/f229.image
- Téléchargement / impression Téléchargement / impression https://gallica.bnf.fr/services/ajax/action/download/ark:/12148/bpt6k6451939t/f229.image
- Mise en scène Mise en scène ×
Mise en scène
Créer facilement :
- Marque-page Marque-page https://gallica.bnf.fr/services/ajax/action/bookmark/ark:/12148/bpt6k6451939t/f229.image ×
Gérer son espace personnel
Ajouter ce document
Ajouter/Voir ses marque-pages
Mes sélections ()Titre - Acheter une reproduction Acheter une reproduction https://gallica.bnf.fr/services/ajax/action/pa-ecommerce/ark:/12148/bpt6k6451939t
- Acheter le livre complet Acheter le livre complet https://gallica.bnf.fr/services/ajax/action/indisponible/achat/ark:/12148/bpt6k6451939t
- Signalement d'anomalie Signalement d'anomalie https://sindbadbnf.libanswers.com/widget_standalone.php?la_widget_id=7142
- Aide Aide https://gallica.bnf.fr/services/ajax/action/aide/ark:/12148/bpt6k6451939t/f229.image × Aide