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)
Stability of approximately quadratic Schwartz distributions. (English) Zbl 1116.39017
Author’s abstract: We consider approximately quadratic distributions in the spirit of the well known Ulam problem and prove that every approximately quadratic distribution can be approximated by a quadratic function.

39B82Stability, separation, extension, and related topics
46F10Operations with distributions (generalized functions)
39B52Functional equations for functions with more general domains and/or ranges
Full Text: DOI
[1] Baker, J. A.: Distributional methods for functional equations. Aequationes math. 62, 136-142 (2001) · Zbl 0989.39009
[2] Cholewa, P. W.: Remarks on the stability of functional equations. Aequationes math. 27, 76-86 (1984) · Zbl 0549.39006
[3] Chung, J.: A distributional version of functional equations and their stabilities. Nonlinear anal. 62, 1037-1051 (2005) · Zbl 1076.39025
[4] Chung, J.: Hyers--Ulam--rassias stability of Cauchy equation in the space of Schwartz distributions. J. math. Anal. appl. 300, 343-350 (2004) · Zbl 1066.39028
[5] Chung, J.: Stability of functional equations in the space of distributions and hyperfunctions. J. math. Anal. appl. 286, 177-186 (2003) · Zbl 1033.39025
[6] Chung, J.; Chung, S. -Y.; Kim, D.: The stability of Cauchy equations in the space of Schwartz distributions. J. math. Anal. appl. 295, 107-114 (2004) · Zbl 1053.39043
[7] Chung, J.; Chung, S. -Y.; Kim, D.: Une caractérisation de l’espace de Schwartz. C. R. Acad. sci. Paris sér. I math. 316, 23-25 (1993)
[8] Czerwik, S.: On the stability of the quadratic mapping in normed spaces. Abh. math. Sem. univ. Hamburg 62, 59-64 (1992) · Zbl 0779.39003
[9] Hörmander, L.: The analysis of linear partial differential operator I. (1983) · Zbl 0521.35001
[10] Matsuzawa, T.: A calculus approach to hyperfunctions III. Nagoya math. J. 118, 133-153 (1990) · Zbl 0692.46042
[11] Rassias, Th.M.: On the stability of functional equations in Banach spaces. J. math. Anal. appl. 251, 264-284 (2000) · Zbl 0964.39026
[12] Rassias, Th.M.: On the stability of linear mapping in Banach spaces. Proc. amer. Math. soc. 72, 297-300 (1978) · Zbl 0398.47040
[13] Schwartz, L.: Théorie des distributions. (1966)
[14] Skof, F.: Proprietá locali e approssimazione di operatori. Rend. sem. Mat. fis. Milano 53, 113-129 (1983)