zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Pre-asymptotic expansions. (English) Zbl 0855.34062
Let {V n } be a sequence of vector spaces with V n+1 V n for n=0,1,2,. A series n=0 v n with v n V n is called a pre-asymptotic expansion of vV 0 , written v n=0 v n with respect to {V n }, if v- n=0 N v n V N+1 for all N. Under suitable assumptions it is shown that the solution v of a linear operator equation Tv=w with vV 0 , w n=0 V n possesses a pre-asymptotic expansion. In particular, for linear differential operators with polynomial coefficients, formal solutions of the form n=0 a n δ (n) (x) can be interpreted as pre-asymptotic expansions of distributional solutions. Sometimes, pre-asymptotic expansions ψ(x) n=0 ψ n (x) are connected with ordinary asymptotic expansions ψ(Ex) n=0 ψ n (Ex) in the sense of ψ(Ex)= n=0 N ψ n (Ex)+o(E N ) for E0.
Reviewer: L.Berg (Rostock)
34E05Asymptotic expansions (ODE)
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
46F10Operations with distributions (generalized functions)