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)
Spectral analysis of Laplacians on the Vicsek set. (English) Zbl 1177.28029
The author obtains a formula, expressed in terms of Chebyshev polynomials, of the spectral decimation function for the standard Laplacian on the $n$-branch Vicsek set, and determines all the forbidden eigenvalues for the Laplacian, where the spectral decimation function is in the sense of {\it T. Shima} [Japan J. Ind. Appl. Math. 13, No. 1, 1--23 (1996; Zbl 0861.58047)]. The author then shows that there exists a gap in the spectrum of the standard Laplacian by verifying the conditions for the criterion for gaps which was obtained earlier by the author. Moreover, he determines the order of the eigenvalues for the Laplacian and describes their asymptotic behavior.

42C99Non-trigonometric Fourier analysis
31C25Dirichlet spaces
Full Text: DOI Link