# zbMATH — the first resource for mathematics

##### Examples
 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.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 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)
Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential. (English) Zbl 1032.35063
Summary: We are interested here in the counting function of resonances $N(h)$ for a perturbation of a periodic Schrödinger operator $P_0$ by decreasing potential $W(hx)$ $(h\searrow 0)$. We obtain a lower bound for $N(h)$ near some singularities of the density of states measure, associated to the unperturbed Hamiltonian $P_0$.

##### MSC:
 35J10 Schrödinger operator 35B34 Resonances in solutions of PDE 35B20 Perturbations (PDE)
##### Keywords:
edges of bands; band crossing
Full Text:
##### References:
 [1] M. Dimassi, M. Zerzeri, A local trace formula for resonances of perturbed periodic Schrödinger operators, J. Funct. Anal., à paraı\hat{}tre · Zbl 1090.35065 [2] Nedelec, L.: Localisation of resonances for matrix Schrödinger operators. Duke math. J. 106, No. 2, 209-236 (2001) · Zbl 1258.35068 [3] Reed, M.; Simon, B.: Methods of modern mathematical physics, analysis operators. (1978) · Zbl 0401.47001 [4] J. Sjöstrand, A trace formula for resonances and application to semi-classical Schrödinger operators, Séminaire équations aux dérivées partielles, Exposé no 11 (1996--97)