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)
Converse problems of Fourier expansion and their applications. (English) Zbl 1044.42006
Summary: Let f𝒞(,H) have a countable frequency set Freq(f) and satisfy Parseval’s equality. We show that if f satisfies one of the following conditions: (a) uniformly continuous and Freq(f) has a unique limit point at infinity; (b) indefinite integral is Lipschitz, Freq(f) converges fast in some sense; (c) in the case of Euclidean space H, all the coefficients are positive, then f is pseudo-almost-periodic. An example is given to show that the conclusion cannot be improved. The results are applied to the theory of Riesz–Fischer and the optimal control theory.
42A75Classical almost periodic functions, mean periodic functions
43A60Almost periodic functions on groups, etc.; almost automorphic functions
49N20Periodic optimization