Matches in SemOpenAlex for { <https://semopenalex.org/work/W2002182592> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W2002182592 abstract "If P is a linear differential operator on Rn with constant coefficients, which is invariant under a group G of linear transformations, it is not true in general that the equation Pu = f always has a G-invariant solution u for a G-invariant f. We elucidate here the particular case of a big group G, and we count the invariant solutions when they exist (see Corollary 28 and Theorems 32, 33). The case, of special interest, of the wave equation and the Lorentz group is covered (Corollary 27). The theory of hyperfunctions provides the frame for the work. Introduction. In his note [61, M. Rais proves that every linear differential operator P on R n with constant coefficients has a tempered fundamental solution invariant under the subgroup of GL(n, R) under which P is invariant: it is a consequence of a theorem of M. F. Atiyah [1]. But it is not true in general that P has an invariant solution of any equation whose second side is invariant by the same group, and M. Rais presents a counterexample where P has degree one. We study here this question. As, in general, when a group acts on a manifold, some orbits are singular (the quotient is not a manifold), one is led naturally to solve an invariant equation first on the open set of the regular orbits, and then to try to extend the solutions: in order to eliminate any artificial obstruction there might be to such an extension, we will work within the frame of the theory of hyperfunctions. To this theory, first developed in [8], one will find a short and excellent introduction in [3]. We have to make precise here what we mean by invariant. This is clear for a function, and therefore for a hyperfunction; for a distribution, there are two possible defmitions: the first extends the definition for functions; the second is the one used in [6, ? 1.41, for which the Dirac measure is invariant under all transformations of the linear group, and for which one has the Received by the editors November 8, 1973 and, in revised form, March 4, 1974. AMS (MOS) subject classifications (1970). Primary 35E99. Copyright" @default.
- W2002182592 created "2016-06-24" @default.
- W2002182592 creator A5051894875 @default.
- W2002182592 date "1975-01-01" @default.
- W2002182592 modified "2023-10-18" @default.
- W2002182592 title "Equations with constant coefficients invariant under a group of linear transformations" @default.
- W2002182592 cites W12298816 @default.
- W2002182592 cites W2004143819 @default.
- W2002182592 cites W2014933473 @default.
- W2002182592 cites W2016027996 @default.
- W2002182592 cites W2082142907 @default.
- W2002182592 cites W2086611696 @default.
- W2002182592 cites W2109860517 @default.
- W2002182592 cites W2159626963 @default.
- W2002182592 cites W2257064673 @default.
- W2002182592 cites W2270684874 @default.
- W2002182592 cites W2288296662 @default.
- W2002182592 cites W2319720267 @default.
- W2002182592 cites W2499402012 @default.
- W2002182592 cites W3038830718 @default.
- W2002182592 cites W602834565 @default.
- W2002182592 doi "https://doi.org/10.1090/s0002-9947-1975-0430501-1" @default.
- W2002182592 hasPublicationYear "1975" @default.
- W2002182592 type Work @default.
- W2002182592 sameAs 2002182592 @default.
- W2002182592 citedByCount "5" @default.
- W2002182592 crossrefType "journal-article" @default.
- W2002182592 hasAuthorship W2002182592A5051894875 @default.
- W2002182592 hasBestOaLocation W20021825921 @default.
- W2002182592 hasConcept C101044782 @default.
- W2002182592 hasConcept C110342517 @default.
- W2002182592 hasConcept C118615104 @default.
- W2002182592 hasConcept C134306372 @default.
- W2002182592 hasConcept C134530390 @default.
- W2002182592 hasConcept C13982400 @default.
- W2002182592 hasConcept C162838799 @default.
- W2002182592 hasConcept C190470478 @default.
- W2002182592 hasConcept C202444582 @default.
- W2002182592 hasConcept C2780012671 @default.
- W2002182592 hasConcept C33923547 @default.
- W2002182592 hasConcept C37914503 @default.
- W2002182592 hasConcept C78045399 @default.
- W2002182592 hasConcept C90119067 @default.
- W2002182592 hasConceptScore W2002182592C101044782 @default.
- W2002182592 hasConceptScore W2002182592C110342517 @default.
- W2002182592 hasConceptScore W2002182592C118615104 @default.
- W2002182592 hasConceptScore W2002182592C134306372 @default.
- W2002182592 hasConceptScore W2002182592C134530390 @default.
- W2002182592 hasConceptScore W2002182592C13982400 @default.
- W2002182592 hasConceptScore W2002182592C162838799 @default.
- W2002182592 hasConceptScore W2002182592C190470478 @default.
- W2002182592 hasConceptScore W2002182592C202444582 @default.
- W2002182592 hasConceptScore W2002182592C2780012671 @default.
- W2002182592 hasConceptScore W2002182592C33923547 @default.
- W2002182592 hasConceptScore W2002182592C37914503 @default.
- W2002182592 hasConceptScore W2002182592C78045399 @default.
- W2002182592 hasConceptScore W2002182592C90119067 @default.
- W2002182592 hasLocation W20021825921 @default.
- W2002182592 hasOpenAccess W2002182592 @default.
- W2002182592 hasPrimaryLocation W20021825921 @default.
- W2002182592 hasRelatedWork W1524253852 @default.
- W2002182592 hasRelatedWork W2007815945 @default.
- W2002182592 hasRelatedWork W2023560165 @default.
- W2002182592 hasRelatedWork W2026079614 @default.
- W2002182592 hasRelatedWork W2059917514 @default.
- W2002182592 hasRelatedWork W2347251357 @default.
- W2002182592 hasRelatedWork W2351019005 @default.
- W2002182592 hasRelatedWork W2351945254 @default.
- W2002182592 hasRelatedWork W2361200949 @default.
- W2002182592 hasRelatedWork W2361602696 @default.
- W2002182592 hasRelatedWork W2365527807 @default.
- W2002182592 hasRelatedWork W2366023836 @default.
- W2002182592 hasRelatedWork W2368453954 @default.
- W2002182592 hasRelatedWork W2369426079 @default.
- W2002182592 hasRelatedWork W2373671884 @default.
- W2002182592 hasRelatedWork W2374044233 @default.
- W2002182592 hasRelatedWork W2375005972 @default.
- W2002182592 hasRelatedWork W2377185001 @default.
- W2002182592 hasRelatedWork W2381011621 @default.
- W2002182592 hasRelatedWork W2390319337 @default.
- W2002182592 isParatext "false" @default.
- W2002182592 isRetracted "false" @default.
- W2002182592 magId "2002182592" @default.
- W2002182592 workType "article" @default.