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)
Spectra of the operator of the first difference in $s_{\alpha},s^0_{\alpha},s^{(c)}_{\alpha}$ and $l_p(\alpha)$ ($1\leq p<\infty$) and application to matrix transformations. (English) Zbl 1157.47027
The author studies the spectra of the operator of the first difference $\Delta$ considered as an operator from $E$ to itself, where $E$ is one of the sets $s_{\alpha}$, $s_{\alpha}^{0}$, $s_{\alpha}^{(c)}$ or $l_{p}(\alpha)$, $1\leq p<\infty$. Then the author applies these results to characterize matrix transformations in $E((\Delta -\lambda I)^{h})$, where $h$ is a complex number. The results of this paper generalize some known results.

47B39Difference operators (operator theory)
47A10Spectrum and resolvent of linear operators
39A70Difference operators
46A45Sequence spaces